Daily Papers

Effective interactive tool use requires agents to master Tool Integrated Reasoning (TIR): a complex process involving multi-turn planning and long-context dialogue management. To train agents for this dynamic process, particularly in multi-modal contexts, we introduce a sandbox environment for reinforcement learning (RL) that supports interleaved speech-text rollouts. Our core strategy, Turn-level Adjudicated Reinforcement Learning (TARL), addresses the challenge of credit assignment in long-horizon tasks by employing a Large Language Model (LLM) as a judge to provide turn-level evaluation. To enhance exploration, we integrate a mixed-task training curriculum with mathematical reasoning problems. This unified approach boosts the task pass rate on the text-based τ-bench by over 6% compared to strong RL baselines. Crucially, we demonstrate our framework's suitability for fine-tuning a multi-modal foundation model for agentic tasks. By training a base multi-modal LLM on interleaved speech-text rollouts, we equip it with tool-use abilities, paving the way for more natural, voice-driven interactive agents.

This paper investigates approaches to enhance the reasoning capabilities of Large Language Model (LLM) agents using Reinforcement Learning (RL). Specifically, we focus on multi-turn tool-use scenarios, which can be naturally modeled as Markov Decision Processes (MDPs). While existing approaches often train multi-turn LLM agents with trajectory-level advantage estimation in bandit settings, they struggle with turn-level credit assignment across multiple decision steps, limiting their performance on multi-turn reasoning tasks. To address this, we introduce a fine-grained turn-level advantage estimation strategy to enable more precise credit assignment in multi-turn agent interactions. The strategy is general and can be incorporated into various RL algorithms such as Group Relative Preference Optimization (GRPO). Our experimental evaluation on multi-turn reasoning and search-based tool-use tasks with GRPO implementations highlights the effectiveness of the MDP framework and the turn-level credit assignment in advancing the multi-turn reasoning capabilities of LLM agents in complex decision-making settings. Our method achieves 100% success in tool execution and 50% accuracy in exact answer matching, significantly outperforming baselines, which fail to invoke tools and achieve only 20-30% exact match accuracy.

Large language model (LLM)-based agents are increasingly trained with reinforcement learning (RL) to enhance their ability to interact with external environments through tool use, particularly in search-based settings that require multi-turn reasoning and knowledge acquisition. However, existing approaches typically rely on outcome-based rewards that are only provided at the final answer. This reward sparsity becomes particularly problematic in multi-turn settings, where long trajectories exacerbate two critical issues: (i) advantage collapse, where all rollouts receive identical rewards and provide no useful learning signals, and (ii) lack of fine-grained credit assignment, where dependencies between turns are obscured, especially in long-horizon tasks. In this paper, we propose Information Gain-based Policy Optimization (IGPO), a simple yet effective RL framework that provides dense and intrinsic supervision for multi-turn agent training. IGPO models each interaction turn as an incremental process of acquiring information about the ground truth, and defines turn-level rewards as the marginal increase in the policy's probability of producing the correct answer. Unlike prior process-level reward approaches that depend on external reward models or costly Monte Carlo estimation, IGPO derives intrinsic rewards directly from the model's own belief updates. These intrinsic turn-level rewards are combined with outcome-level supervision to form dense reward trajectories. Extensive experiments on both in-domain and out-of-domain benchmarks demonstrate that IGPO consistently outperforms strong baselines in multi-turn scenarios, achieving higher accuracy and improved sample efficiency.

Goal-conditioned hierarchical reinforcement learning (HRL) is a promising approach for scaling up reinforcement learning (RL) techniques. However, it often suffers from training inefficiency as the action space of the high-level, i.e., the goal space, is often large. Searching in a large goal space poses difficulties for both high-level subgoal generation and low-level policy learning. In this paper, we show that this problem can be effectively alleviated by restricting the high-level action space from the whole goal space to a k-step adjacent region of the current state using an adjacency constraint. We theoretically prove that the proposed adjacency constraint preserves the optimal hierarchical policy in deterministic MDPs, and show that this constraint can be practically implemented by training an adjacency network that can discriminate between adjacent and non-adjacent subgoals. Experimental results on discrete and continuous control tasks show that incorporating the adjacency constraint improves the performance of state-of-the-art HRL approaches in both deterministic and stochastic environments.

Training Large Language Models (LLMs) for multi-turn Tool-Integrated Reasoning (TIR) - where models iteratively reason, generate code, and verify through execution - remains challenging for existing reinforcement learning (RL) approaches. Current RL methods, exemplified by Group Relative Policy Optimization (GRPO), suffer from coarse-grained, trajectory-level rewards that provide insufficient learning signals for complex multi-turn interactions, leading to training stagnation. To address this issue, we propose Group Turn Policy Optimization (GTPO), a novel RL algorithm specifically designed for training LLMs on multi-turn TIR tasks. GTPO introduces three key innovations: (1) turn-level reward assignment that provides fine-grained feedback for individual turns, (2) return-based advantage estimation where normalized discounted returns are calculated as advantages, and (3) self-supervised reward shaping that exploits self-supervision signals from generated code to densify sparse binary outcome-based rewards. Our comprehensive evaluation demonstrates that GTPO outperforms GRPO by 3.0% on average across diverse reasoning benchmarks, establishing its effectiveness for advancing complex mathematical reasoning in the real world.

A broad use case of large language models (LLMs) is in goal-directed decision-making tasks (or "agent" tasks), where an LLM needs to not just generate completions for a given prompt, but rather make intelligent decisions over a multi-turn interaction to accomplish a task (e.g., when interacting with the web, using tools, or providing customer support). Reinforcement learning (RL) provides a general paradigm to address such agent tasks, but current RL methods for LLMs largely focus on optimizing single-turn rewards. By construction, most single-turn RL methods cannot endow LLMs with the ability to intelligently seek information over multiple turns, perform credit assignment, or reason about their past actions -- all of which are critical in agent tasks. This raises the question: how can we design effective and efficient multi-turn RL algorithms for LLMs? In this paper, we develop a framework for building multi-turn RL algorithms for fine-tuning LLMs, that preserves the flexibility of existing single-turn RL methods for LLMs (e.g., proximal policy optimization), while accommodating multiple turns, long horizons, and delayed rewards effectively. To do this, our framework adopts a hierarchical RL approach and runs two RL algorithms in parallel: a high-level off-policy value-based RL algorithm to aggregate reward over utterances, and a low-level RL algorithm that utilizes this high-level value function to train a token policy within each utterance or turn. Our hierarchical framework, Actor-Critic Framework with a Hierarchical Structure (ArCHer), can also give rise to other RL methods. Empirically, we find that ArCHer significantly improves efficiency and performance on agent tasks, attaining a sample efficiency of about 100x over existing methods, while also improving with larger model capacity (upto the 7 billion scale that we tested on).

Large-scale reinforcement learning with verifiable rewards (RLVR) has demonstrated its effectiveness in harnessing the potential of large language models (LLMs) for single-turn reasoning tasks. In realistic reasoning scenarios, LLMs can often utilize external tools to assist in task-solving processes. However, current RL algorithms inadequately balance the models' intrinsic long-horizon reasoning capabilities and their proficiency in multi-turn tool interactions. To bridge this gap, we propose Agentic Reinforced Policy Optimization (ARPO), a novel agentic RL algorithm tailored for training multi-turn LLM-based agents. Through preliminary experiments, we observe that LLMs tend to exhibit highly uncertain behavior, characterized by an increase in the entropy distribution of generated tokens, immediately following interactions with external tools. Motivated by this observation, ARPO incorporates an entropy-based adaptive rollout mechanism, dynamically balancing global trajectory sampling and step-level sampling, thereby promoting exploration at steps with high uncertainty after tool usage. By integrating an advantage attribution estimation, ARPO enables LLMs to internalize advantage differences in stepwise tool-use interactions. Our experiments across 13 challenging benchmarks in computational reasoning, knowledge reasoning, and deep search domains demonstrate ARPO's superiority over trajectory-level RL algorithms. Remarkably, ARPO achieves improved performance using only half of the tool-use budget required by existing methods, offering a scalable solution for aligning LLM-based agents with real-time dynamic environments. Our code and datasets are released at https://github.com/dongguanting/ARPO

Goal-conditioned Hierarchical Reinforcement Learning (HRL) is a promising approach for scaling up reinforcement learning (RL) techniques. However, it often suffers from training inefficiency as the action space of the high-level, i.e., the goal space, is large. Searching in a large goal space poses difficulty for both high-level subgoal generation and low-level policy learning. In this paper, we show that this problem can be effectively alleviated by restricting the high-level action space from the whole goal space to a k-step adjacent region of the current state using an adjacency constraint. We theoretically prove that in a deterministic Markov Decision Process (MDP), the proposed adjacency constraint preserves the optimal hierarchical policy, while in a stochastic MDP the adjacency constraint induces a bounded state-value suboptimality determined by the MDP's transition structure. We further show that this constraint can be practically implemented by training an adjacency network that can discriminate between adjacent and non-adjacent subgoals. Experimental results on discrete and continuous control tasks including challenging simulated robot locomotion and manipulation tasks show that incorporating the adjacency constraint significantly boosts the performance of state-of-the-art goal-conditioned HRL approaches.

Recently, extensive studies in Reinforcement Learning have been carried out on the ability of transformers to adapt in-context to various environments and tasks. Current in-context RL methods are limited by their strict requirements for data, which needs to be generated by RL agents or labeled with actions from an optimal policy. In order to address this prevalent problem, we propose AD^varepsilon, a new data acquisition approach that enables in-context Reinforcement Learning from noise-induced curriculum. We show that it is viable to construct a synthetic noise injection curriculum which helps to obtain learning histories. Moreover, we experimentally demonstrate that it is possible to alleviate the need for generation using optimal policies, with in-context RL still able to outperform the best suboptimal policy in a learning dataset by a 2x margin.

Recently, reward-conditioned reinforcement learning (RCRL) has gained popularity due to its simplicity, flexibility, and off-policy nature. However, we will show that current RCRL approaches are fundamentally limited and fail to address two critical challenges of RCRL -- improving generalization on high reward-to-go (RTG) inputs, and avoiding out-of-distribution (OOD) RTG queries during testing time. To address these challenges when training vanilla RCRL architectures, we propose Bayesian Reparameterized RCRL (BR-RCRL), a novel set of inductive biases for RCRL inspired by Bayes' theorem. BR-RCRL removes a core obstacle preventing vanilla RCRL from generalizing on high RTG inputs -- a tendency that the model treats different RTG inputs as independent values, which we term ``RTG Independence". BR-RCRL also allows us to design an accompanying adaptive inference method, which maximizes total returns while avoiding OOD queries that yield unpredictable behaviors in vanilla RCRL methods. We show that BR-RCRL achieves state-of-the-art performance on the Gym-Mujoco and Atari offline RL benchmarks, improving upon vanilla RCRL by up to 11%.

Recent advances in large multimodal models have leveraged image-based tools with reinforcement learning to tackle visual problems. However, existing open-source approaches often exhibit monotonous reasoning patterns and allow only a limited number of interaction turns, making them inadequate for difficult tasks that require trial-and-error exploration. In this work, we address this limitation by scaling up tool-based interactions and introduce Mini-o3, a system that executes deep, multi-turn reasoning -- spanning tens of steps -- and achieves state-of-the-art performance on challenging visual search tasks. Our recipe for reproducing OpenAI o3-style behaviors comprises three key components. First, we construct the Visual Probe Dataset, a collection of thousands of challenging visual search problems designed for exploratory reasoning. Second, we develop an iterative data collection pipeline to obtain cold-start trajectories that exhibit diverse reasoning patterns, including depth-first search, trial-and-error, and goal maintenance. Third, we propose an over-turn masking strategy that prevents penalization of over-turn responses (those that hit the maximum number of turns) during reinforcement learning, thereby balancing training-time efficiency with test-time scalability. Despite training with an upper bound of only six interaction turns, our model generates trajectories that naturally scale to tens of turns at inference time, with accuracy improving as the number of turns increases. Extensive experiments demonstrate that Mini-o3 produces rich reasoning patterns and deep thinking paths, effectively solving challenging visual search problems.

Hierarchical reinforcement learning (RL) can accelerate long-horizon decision-making by temporally abstracting a policy into multiple levels. Promising results in sparse reward environments have been seen with skills, i.e. sequences of primitive actions. Typically, a skill latent space and policy are discovered from offline data, but the resulting low-level policy can be unreliable due to low-coverage demonstrations or distribution shifts. As a solution, we propose fine-tuning the low-level policy in conjunction with high-level skill selection. Our Skill-Critic algorithm optimizes both the low and high-level policies; these policies are also initialized and regularized by the latent space learned from offline demonstrations to guide the joint policy optimization. We validate our approach in multiple sparse RL environments, including a new sparse reward autonomous racing task in Gran Turismo Sport. The experiments show that Skill-Critic's low-level policy fine-tuning and demonstration-guided regularization are essential for optimal performance. Images and videos are available at https://sites.google.com/view/skill-critic. We plan to open source the code with the final version.

Training large language models (LLMs) as interactive agents for controlling graphical user interfaces (GUIs) presents a unique challenge to optimize long-horizon action sequences with multimodal feedback from complex environments. While recent works have advanced multi-turn reinforcement learning (RL) for reasoning and tool-using capabilities in LLMs, their application to GUI-based agents remains relatively underexplored due to the difficulty of sparse rewards, delayed feedback, and high rollout costs. In this paper, we investigate end-to-end policy optimization for vision-language-based GUI agents with the aim of improving performance on complex, long-horizon computer tasks. We propose Agentic Replay Policy Optimization (ARPO), an end-to-end RL approach that augments Group Relative Policy Optimization (GRPO) with a replay buffer to reuse the successful experience across training iterations. To further stabilize the training process, we propose a task selection strategy that filters tasks based on baseline agent performance, allowing the agent to focus on learning from informative interactions. Additionally, we compare ARPO with offline preference optimization approaches, highlighting the advantages of policy-based methods in GUI environments. Experiments on the OSWorld benchmark demonstrate that ARPO achieves competitive results, establishing a new performance baseline for LLM-based GUI agents trained via reinforcement learning. Our findings underscore the effectiveness of reinforcement learning for training multi-turn, vision-language GUI agents capable of managing complex real-world UI interactions. Codes and models:https://github.com/dvlab-research/ARPO.git.

Research on applications of Reinforcement Learning (RL) to Large Language Models (LLMs) has mostly been focused on single-turn problems, such as mathematical reasoning or single-shot code generation. While these problems can be viewed as token-level multi-turn MDPs, this view corresponds to a degenerate case of multi-turn interaction where the environment provides no feedback. This contrasts with many real-world domains, such as software engineering (SWE), which require rich multi-turn interactions with a stateful environment that responds to each action with a non-trivial observation. To bridge this gap, we demonstrate the successful application of RL to this general regime. Using a modified Decoupled Advantage Policy Optimization (DAPO) algorithm, we train an agent based on Qwen2.5-72B-Instruct to solve real-world software engineering tasks. Our approach increases the agent's success rate on the SWE-bench Verified benchmark from a 20% rejection fine-tuned baseline to 39%, without relying on any teacher models. On SWE-rebench, our agent matches or outperforms leading open-weight models such as DeepSeek-V3-0324 and Qwen3-235B-A22B using an identical scaffolding, offering a viable path toward building more capable autonomous agents for complex real-world problems based on open models.

Outcome-driven reinforcement learning has advanced reasoning in large language models (LLMs), but prevailing tool-augmented approaches train a single, monolithic policy that interleaves thoughts and tool calls under full context; this scales poorly with long horizons and diverse tools and generalizes weakly to new scenarios. Agentic systems offer a promising alternative by decomposing work across specialized modules, yet most remain training-free or rely on offline training decoupled from the live dynamics of multi-turn interaction. We introduce AgentFlow, a trainable, in-the-flow agentic framework that coordinates four modules (planner, executor, verifier, generator) through an evolving memory and directly optimizes its planner inside the multi-turn loop. To train on-policy in live environments, we propose Flow-based Group Refined Policy Optimization (Flow-GRPO), which tackles long-horizon, sparse-reward credit assignment by converting multi-turn optimization into a sequence of tractable single-turn policy updates. It broadcasts a single, verifiable trajectory-level outcome to every turn to align local planner decisions with global success and stabilizes learning with group-normalized advantages. Across ten benchmarks, AgentFlow with a 7B-scale backbone outperforms top-performing baselines with average accuracy gains of 14.9% on search, 14.0% on agentic, 14.5% on mathematical, and 4.1% on scientific tasks, even surpassing larger proprietary models like GPT-4o. Further analyses confirm the benefits of in-the-flow optimization, showing improved planning, enhanced tool-calling reliability, and positive scaling with model size and reasoning turns.

Reinforcement learning from Human Feedback (RLHF) learns from preference signals, while standard Reinforcement Learning (RL) directly learns from reward signals. Preferences arguably contain less information than rewards, which makes preference-based RL seemingly more difficult. This paper theoretically proves that, for a wide range of preference models, we can solve preference-based RL directly using existing algorithms and techniques for reward-based RL, with small or no extra costs. Specifically, (1) for preferences that are drawn from reward-based probabilistic models, we reduce the problem to robust reward-based RL that can tolerate small errors in rewards; (2) for general arbitrary preferences where the objective is to find the von Neumann winner, we reduce the problem to multiagent reward-based RL which finds Nash equilibria for factored Markov games under a restricted set of policies. The latter case can be further reduce to adversarial MDP when preferences only depend on the final state. We instantiate all reward-based RL subroutines by concrete provable algorithms, and apply our theory to a large class of models including tabular MDPs and MDPs with generic function approximation. We further provide guarantees when K-wise comparisons are available.

Multi-step learning applies lookahead over multiple time steps and has proved valuable in policy evaluation settings. However, in the optimal control case, the impact of multi-step learning has been relatively limited despite a number of prior efforts. Fundamentally, this might be because multi-step policy improvements require operations that cannot be approximated by stochastic samples, hence hindering the widespread adoption of such methods in practice. To address such limitations, we introduce doubly multi-step off-policy VI (DoMo-VI), a novel oracle algorithm that combines multi-step policy improvements and policy evaluations. DoMo-VI enjoys guaranteed convergence speed-up to the optimal policy and is applicable in general off-policy learning settings. We then propose doubly multi-step off-policy actor-critic (DoMo-AC), a practical instantiation of the DoMo-VI algorithm. DoMo-AC introduces a bias-variance trade-off that ensures improved policy gradient estimates. When combined with the IMPALA architecture, DoMo-AC has showed improvements over the baseline algorithm on Atari-57 game benchmarks.

Training LLM agents in multi-turn environments with sparse rewards, where completing a single task requires 30+ turns of interaction within an episode, presents a fundamental challenge for reinforcement learning. We identify a critical failure mode unique to this setting: the exploration-exploitation cascade failure. This cascade begins with early-stage policy premature convergence, where sparse feedback causes agents to commit to flawed, low-entropy strategies. Subsequently, agents enter late-stage policy collapse, where conventional entropy regularization becomes counterproductive, promoting chaotic exploration that destabilizes training. We propose Entropy-regularized Policy Optimization (EPO), a general framework that breaks this failure cycle through three synergistic mechanisms: (1) adopting entropy regularization in multi-turn settings to enhance exploration, (2) an entropy smoothing regularizer that bounds policy entropy within historical averages to prevent abrupt fluctuations, and (3) adaptive phase-based weighting that balances exploration and exploitation across training. Our analysis justifies that EPO guarantees monotonically decreasing entropy variance while maintaining convergence. EPO achieves up to 152% performance improvement on ScienceWorld and up to 19.8% on ALFWorld. Our work demonstrates that multi-turn sparse-reward settings require fundamentally different entropy control than traditional RL, with broad implications for LLM agent training.

Behavior constrained policy optimization has been demonstrated to be a successful paradigm for tackling Offline Reinforcement Learning. By exploiting historical transitions, a policy is trained to maximize a learned value function while constrained by the behavior policy to avoid a significant distributional shift. In this paper, we propose our closed-form policy improvement operators. We make a novel observation that the behavior constraint naturally motivates the use of first-order Taylor approximation, leading to a linear approximation of the policy objective. Additionally, as practical datasets are usually collected by heterogeneous policies, we model the behavior policies as a Gaussian Mixture and overcome the induced optimization difficulties by leveraging the LogSumExp's lower bound and Jensen's Inequality, giving rise to a closed-form policy improvement operator. We instantiate offline RL algorithms with our novel policy improvement operators and empirically demonstrate their effectiveness over state-of-the-art algorithms on the standard D4RL benchmark. Our code is available at https://cfpi-icml23.github.io/.

Reinforcement learning (RL) has shown promise in training agentic models that move beyond static benchmarks to engage in dynamic, multi-turn interactions. Yet, the ultimate value of such agents lies in their ability to assist users, a setting where diversity and dynamics of user interaction pose challenges. In this work, we propose UserRL, a unified framework for training and evaluating user-centric abilities through standardized gym environments paired with simulated users. We systematically vary turn-level reward assignment and trajectory-level score calculation to analyze how different formulations affect learning under the GRPO algorithm. Our experiments across Qwen3 models reveal three key findings: (i) SFT cold start is critical for unlocking initial interaction ability and enabling sustained RL improvements; (ii) deliberate trajectory scoring yields more efficient and effective multi-turn interactions; and (iii) while stronger simulated users (e.g., GPT-4o) facilitates training, open-source simulators (e.g., Qwen3-32B) remain a cost-effective and transferable option. Together, these results highlight that careful design of reward shaping and user simulation choice is as crucial as model scale, and establish UserRL as a practical pathway for developing robust user-centric agentic models. All codes and data are public for future research.

Learning from Demonstration (LfD) aims to facilitate rapid Reinforcement Learning (RL) by leveraging expert demonstrations to pre-train the RL agent. However, the limited availability of expert demonstration data often hinders its ability to effectively aid downstream RL learning. To address this problem, we propose a novel two-stage method dubbed as Skill-enhanced Reinforcement Learning Acceleration (SeRLA). SeRLA introduces a skill-level adversarial Positive-Unlabeled (PU) learning model to extract useful skill prior knowledge by enabling learning from both limited expert data and general low-cost demonstration data in the offline prior learning stage. Subsequently, it deploys a skill-based soft actor-critic algorithm to leverage this acquired prior knowledge in the downstream online RL stage for efficient training of a skill policy network. Moreover, we develop a simple skill-level data enhancement technique to further alleviate data sparsity and improve both skill prior learning and downstream skill policy training. Our experimental results on multiple standard RL environments show the proposed SeRLA method achieves state-of-the-art performance on accelerating reinforcement learning on downstream tasks, especially in the early learning phase.

Reinforcement Learning with Verifiable Rewards (RLVR) has advanced the reasoning capability of large language models (LLMs), enabling autonomous agents that can conduct effective multi-turn and tool-integrated reasoning. While instructions serve as the primary protocol for defining agents, RLVR typically relies on static and manually designed instructions. However, those instructions may be suboptimal for the base model, and the optimal instruction may change as the agent's policy improves and explores the interaction with the environment. To bridge the gap, we introduce INSPO, a novel Instruction-Policy co-evolution framework that integrates instruction optimization as a dynamic component of the reinforcement learning (RL) loop. INSPO maintains a dynamic population of instruction candidates that are sampled with questions, where reward signals in RL loops are automatically attributed to each instruction, and low performers are periodically pruned. New instructions are generated and verified through an on-policy reflection mechanism, where an LLM-based optimizer analyzes past experience from a replay buffer and evolves more effective strategies given the current policy. We conduct extensive experiments on multi-turn retrieval and reasoning tasks, demonstrating that INSPO substantially outperforms strong baselines relying on static instructions. INSPO discovers innovative instructions that guide the agent toward more strategic reasoning paths, achieving substantial performance gains with only a marginal increase in computational overhead.

The ability to plan actions on multiple levels of abstraction enables intelligent agents to solve complex tasks effectively. However, learning the models for both low and high-level planning from demonstrations has proven challenging, especially with higher-dimensional inputs. To address this issue, we propose to use reinforcement learning to identify subgoals in expert trajectories by associating the magnitude of the rewards with the predictability of low-level actions given the state and the chosen subgoal. We build a vector-quantized generative model for the identified subgoals to perform subgoal-level planning. In experiments, the algorithm excels at solving complex, long-horizon decision-making problems outperforming state-of-the-art. Because of its ability to plan, our algorithm can find better trajectories than the ones in the training set

Reinforcement learning for LLM reasoning has rapidly emerged as a prominent research area, marked by a significant surge in related studies on both algorithmic innovations and practical applications. Despite this progress, several critical challenges remain, including the absence of standardized guidelines for employing RL techniques and a fragmented understanding of their underlying mechanisms. Additionally, inconsistent experimental settings, variations in training data, and differences in model initialization have led to conflicting conclusions, obscuring the key characteristics of these techniques and creating confusion among practitioners when selecting appropriate techniques. This paper systematically reviews widely adopted RL techniques through rigorous reproductions and isolated evaluations within a unified open-source framework. We analyze the internal mechanisms, applicable scenarios, and core principles of each technique through fine-grained experiments, including datasets of varying difficulty, model sizes, and architectures. Based on these insights, we present clear guidelines for selecting RL techniques tailored to specific setups, and provide a reliable roadmap for practitioners navigating the RL for the LLM domain. Finally, we reveal that a minimalist combination of two techniques can unlock the learning capability of critic-free policies using vanilla PPO loss. The results demonstrate that our simple combination consistently improves performance, surpassing strategies like GRPO and DAPO.

Training large language models (LLMs) as interactive agents presents unique challenges including long-horizon decision making and interacting with stochastic environment feedback. While reinforcement learning (RL) has enabled progress in static tasks, multi-turn agent RL training remains underexplored. We propose StarPO (State-Thinking-Actions-Reward Policy Optimization), a general framework for trajectory-level agent RL, and introduce RAGEN, a modular system for training and evaluating LLM agents. Our study on three stylized environments reveals three core findings. First, our agent RL training shows a recurring mode of Echo Trap where reward variance cliffs and gradient spikes; we address this with StarPO-S, a stabilized variant with trajectory filtering, critic incorporation, and decoupled clipping. Second, we find the shaping of RL rollouts would benefit from diverse initial states, medium interaction granularity and more frequent sampling. Third, we show that without fine-grained, reasoning-aware reward signals, agent reasoning hardly emerge through multi-turn RL and they may show shallow strategies or hallucinated thoughts. Code and environments are available at https://github.com/RAGEN-AI/RAGEN.

A major challenge in Reinforcement Learning (RL) is the difficulty of learning an optimal policy from sparse rewards. Prior works enhance online RL with conventional Imitation Learning (IL) via a handcrafted auxiliary objective, at the cost of restricting the RL policy to be sub-optimal when the offline data is generated by a non-expert policy. Instead, to better leverage valuable information in offline data, we develop Generalized Imitation Learning from Demonstration (GILD), which meta-learns an objective that distills knowledge from offline data and instills intrinsic motivation towards the optimal policy. Distinct from prior works that are exclusive to a specific RL algorithm, GILD is a flexible module intended for diverse vanilla off-policy RL algorithms. In addition, GILD introduces no domain-specific hyperparameter and minimal increase in computational cost. In four challenging MuJoCo tasks with sparse rewards, we show that three RL algorithms enhanced with GILD significantly outperform state-of-the-art methods.

Social agents powered by large language models (LLMs) can simulate human social behaviors but fall short in handling complex goal-oriented social dialogues. Direct Preference Optimization (DPO) has proven effective in aligning LLM behavior with human preferences across a variety of agent tasks. Existing DPO-based approaches for multi-turn interactions are divided into turn-level and session-level methods. The turn-level method is overly fine-grained, focusing exclusively on individual turns, while session-level methods are too coarse-grained, often introducing training noise. To address these limitations, we propose Segment-Level Direct Preference Optimization (SDPO), which focuses on specific key segments within interactions to optimize multi-turn agent behavior while minimizing training noise. Evaluations on the SOTOPIA benchmark demonstrate that SDPO-tuned agents consistently outperform both existing DPO-based methods and proprietary LLMs like GPT-4o, underscoring SDPO's potential to advance the social intelligence of LLM-based agents. We release our code and data at https://github.com/AlibabaResearch/DAMO-ConvAI/tree/main/SDPO.

Offline goal-conditioned reinforcement learning (GCRL) offers a practical learning paradigm where goal-reaching policies are trained from abundant unlabeled (reward-free) datasets without additional environment interaction. However, offline GCRL still struggles with long-horizon tasks, even with recent advances that employ hierarchical policy structures, such as HIQL. By identifying the root cause of this challenge, we observe the following insights: First, performance bottlenecks mainly stem from the high-level policy's inability to generate appropriate subgoals. Second, when learning the high-level policy in the long-horizon regime, the sign of the advantage signal frequently becomes incorrect. Thus, we argue that improving the value function to produce a clear advantage signal for learning the high-level policy is essential. In this paper, we propose a simple yet effective solution: Option-aware Temporally Abstracted value learning, dubbed OTA, which incorporates temporal abstraction into the temporal-difference learning process. By modifying the value update to be option-aware, the proposed learning scheme contracts the effective horizon length, enabling better advantage estimates even in long-horizon regimes. We experimentally show that the high-level policy extracted using the OTA value function achieves strong performance on complex tasks from OGBench, a recently proposed offline GCRL benchmark, including maze navigation and visual robotic manipulation environments.

Uniform random exploration in decision-making systems supports off-policy learning via supervision but incurs high regret, making it impractical for many applications. Conversely, non-uniform exploration offers better immediate performance but lacks support for off-policy learning. Recent research suggests that regression oracles can bridge this gap by combining non-uniform exploration with supervised learning. In this paper, we analyze these approaches within a real-world industrial context at Adyen, a large global payments processor characterized by batch logged delayed feedback, short-term memory, and dynamic action spaces under the Empirical Risk Minimization (ERM) framework. Our analysis reveals that while regression oracles significantly improve performance, they introduce challenges due to rigid algorithmic assumptions. Specifically, we observe that as a policy improves, subsequent generations may perform worse due to shifts in the reward distribution and increased class imbalance in the training data. This degradation occurs de spite improvements in other aspects of the training data, leading to decreased performance in successive policy iterations. We further explore the long-term impact of regression oracles, identifying a potential "oscillation effect." This effect arises when regression oracles influence probability estimates and the realizability of subsequent policy models, leading to fluctuations in performance across iterations. Our findings highlight the need for more adaptable algorithms that can leverage the benefits of regression oracles without introducing instability in policy performance over time.

Interactive digital agents (IDAs) leverage APIs of stateful digital environments to perform tasks in response to user requests. While IDAs powered by instruction-tuned large language models (LLMs) can react to feedback from interface invocations in multi-step exchanges, they have not been trained in their respective digital environments. Prior methods accomplish less than half of tasks in sophisticated benchmarks such as AppWorld. We present a reinforcement learning (RL) approach that trains IDAs directly in their target environments. We formalize this training as a partially observable Markov decision process and derive LOOP, a data- and memory-efficient variant of proximal policy optimization. LOOP uses no value network and maintains exactly one copy of the underlying LLM in memory, making its implementation straightforward and as memory-efficient as fine-tuning a single LLM. A 32-billion-parameter agent trained with LOOP in the AppWorld environment outperforms the much larger OpenAI o1 agent by 9 percentage points (15% relative). To our knowledge, this is the first reported application of RL to IDAs that interact with a stateful, multi-domain, multi-app environment via direct API calls. Our analysis sheds light on the effectiveness of RL in this area, showing that the agent learns to consult the API documentation, avoid unwarranted assumptions, minimize confabulation, and recover from setbacks.

The generative power of diffusion models (DMs) has recently enabled high-performing decision-making algorithms in offline reinforcement learning (RL), achieving state-of-the-art results across standard benchmarks. Among them, Diffusion Q-Learning (DQL) stands out as a leading method for its consistently strong performance. Nevertheless, DQL remains limited in practice due to its reliance on multi-step denoising for action generation during both training and inference. Although one-step denoising is desirable, simply applying it to DQL leads to a drastic performance drop. In this work, we revisit DQL and identify its core limitations. We then propose One-Step Flow Q-Learning (OFQL), a novel framework that enables efficient one-step action generation during both training and inference, without requiring auxiliary models, distillation, or multi-phase training. Specifically, OFQL reformulates DQL within the sample-efficient Flow Matching (FM) framework. While conventional FM induces curved generative trajectories that impede one-step generation, OFQL instead learns an average velocity field that facilitates direct, accurate action generation. Collectively, OFQL eliminates the need for multi-step sampling and recursive gradient updates in DQL, resulting in faster and more robust training and inference. Extensive experiments on the D4RL benchmark demonstrate that OFQL outperforms DQL and other diffusion-based baselines, while substantially reducing both training and inference time compared to DQL.

Decision Transformer (DT) is an innovative algorithm leveraging recent advances of the transformer architecture in reinforcement learning (RL). However, a notable limitation of DT is its reliance on recalling trajectories from datasets, losing the capability to seamlessly stitch sub-optimal trajectories together. In this work we introduce a general sequence modeling framework for studying sequential decision making through the lens of Hierarchical RL. At the time of making decisions, a high-level policy first proposes an ideal prompt for the current state, a low-level policy subsequently generates an action conditioned on the given prompt. We show DT emerges as a special case of this framework with certain choices of high-level and low-level policies, and discuss the potential failure of these choices. Inspired by these observations, we study how to jointly optimize the high-level and low-level policies to enable the stitching ability, which further leads to the development of new offline RL algorithms. Our empirical results clearly show that the proposed algorithms significantly surpass DT on several control and navigation benchmarks. We hope our contributions can inspire the integration of transformer architectures within the field of RL.

Recent advances in reinforcement learning (RL) with verifiable outcome rewards have significantly improved the reasoning capabilities of large language models (LLMs), especially when combined with multi-turn tool interactions. However, existing methods lack both meaningful verification signals from realistic environments and explicit optimization for verification, leading to unreliable self-verification. To address these limitations, we propose ReVeal, a multi-turn reinforcement learning framework that interleaves code generation with explicit self-verification and tool-based evaluation. ReVeal enables LLMs to autonomously generate test cases, invoke external tools for precise feedback, and improves performance via a customized RL algorithm with dense, per-turn rewards. As a result, ReVeal fosters the co-evolution of a model's generation and verification capabilities through RL training, expanding the reasoning boundaries of the base model, demonstrated by significant gains in Pass@k on LiveCodeBench. It also enables test-time scaling into deeper inference regimes, with code consistently evolving as the number of turns increases during inference, ultimately surpassing DeepSeek-R1-Zero-Qwen-32B. These findings highlight the promise of ReVeal as a scalable and effective paradigm for building more robust and autonomous AI agents.

MDPs with low-rank transitions -- that is, the transition matrix can be factored into the product of two matrices, left and right -- is a highly representative structure that enables tractable learning. The left matrix enables expressive function approximation for value-based learning and has been studied extensively. In this work, we instead investigate sample-efficient learning with density features, i.e., the right matrix, which induce powerful models for state-occupancy distributions. This setting not only sheds light on leveraging unsupervised learning in RL, but also enables plug-in solutions for convex RL. In the offline setting, we propose an algorithm for off-policy estimation of occupancies that can handle non-exploratory data. Using this as a subroutine, we further devise an online algorithm that constructs exploratory data distributions in a level-by-level manner. As a central technical challenge, the additive error of occupancy estimation is incompatible with the multiplicative definition of data coverage. In the absence of strong assumptions like reachability, this incompatibility easily leads to exponential error blow-up, which we overcome via novel technical tools. Our results also readily extend to the representation learning setting, when the density features are unknown and must be learned from an exponentially large candidate set.

Many existing reinforcement learning (RL) methods employ stochastic gradient iteration on the back end, whose stability hinges upon a hypothesis that the data-generating process mixes exponentially fast with a rate parameter that appears in the step-size selection. Unfortunately, this assumption is violated for large state spaces or settings with sparse rewards, and the mixing time is unknown, making the step size inoperable. In this work, we propose an RL methodology attuned to the mixing time by employing a multi-level Monte Carlo estimator for the critic, the actor, and the average reward embedded within an actor-critic (AC) algorithm. This method, which we call Multi-level Actor-Critic (MAC), is developed especially for infinite-horizon average-reward settings and neither relies on oracle knowledge of the mixing time in its parameter selection nor assumes its exponential decay; it, therefore, is readily applicable to applications with slower mixing times. Nonetheless, it achieves a convergence rate comparable to the state-of-the-art AC algorithms. We experimentally show that these alleviated restrictions on the technical conditions required for stability translate to superior performance in practice for RL problems with sparse rewards.

On-policy reinforcement learning (RL) has become a popular framework for solving sequential decision problems due to its computational efficiency and theoretical simplicity. Some on-policy methods guarantee every policy update is constrained to a trust region relative to the prior policy to ensure training stability. These methods often require computationally intensive non-linear optimization or require a particular form of action distribution. In this work, we show that applying KL penalization alone is nearly sufficient to enforce such trust regions. Then, we show that introducing a "fixup" phase is sufficient to guarantee a trust region is enforced on every policy update while adding fewer than 5% additional gradient steps in practice. The resulting algorithm, which we call FixPO, is able to train a variety of policy architectures and action spaces, is easy to implement, and produces results competitive with other trust region methods.

In offline reinforcement learning, the challenge of out-of-distribution (OOD) is pronounced. To address this, existing methods often constrain the learned policy through policy regularization. However, these methods often suffer from the issue of unnecessary conservativeness, hampering policy improvement. This occurs due to the indiscriminate use of all actions from the behavior policy that generates the offline dataset as constraints. The problem becomes particularly noticeable when the quality of the dataset is suboptimal. Thus, we propose Adaptive Advantage-guided Policy Regularization (A2PR), obtaining high-advantage actions from an augmented behavior policy combined with VAE to guide the learned policy. A2PR can select high-advantage actions that differ from those present in the dataset, while still effectively maintaining conservatism from OOD actions. This is achieved by harnessing the VAE capacity to generate samples matching the distribution of the data points. We theoretically prove that the improvement of the behavior policy is guaranteed. Besides, it effectively mitigates value overestimation with a bounded performance gap. Empirically, we conduct a series of experiments on the D4RL benchmark, where A2PR demonstrates state-of-the-art performance. Furthermore, experimental results on additional suboptimal mixed datasets reveal that A2PR exhibits superior performance. Code is available at https://github.com/ltlhuuu/A2PR.

Progress in many task domains emerges from repeated revisions to previous solution attempts. Training agents that can reliably self-improve over such sequences at inference-time is a natural target for reinforcement learning (RL), yet the naive approach assumes a fixed maximum iteration depth, which can be both costly and arbitrary. We present Exploratory Iteration (ExIt), a family of autocurriculum RL methods that directly exploits the recurrent structure of self-improvement tasks to train LLMs to perform multi-step self-improvement at inference-time while only training on the most informative single-step iterations. ExIt grows a task space by selectively sampling the most informative intermediate, partial histories encountered during an episode for continued iteration, treating these starting points as new self-iteration task instances to train a self-improvement policy. ExIt can further pair with explicit exploration mechanisms to sustain greater task diversity. Across several domains, encompassing competition math, multi-turn tool-use, and machine learning engineering, we demonstrate that ExIt strategies, starting from either a single or many task instances, can produce policies exhibiting strong inference-time self-improvement on held-out task instances, and the ability to iterate towards higher performance over a step budget extending beyond the average iteration depth encountered during training.

In reinforcement learning (RL), rewards of states are typically considered additive, and following the Markov assumption, they are independent of states visited previously. In many important applications, such as coverage control, experiment design and informative path planning, rewards naturally have diminishing returns, i.e., their value decreases in light of similar states visited previously. To tackle this, we propose submodular RL (SubRL), a paradigm which seeks to optimize more general, non-additive (and history-dependent) rewards modelled via submodular set functions which capture diminishing returns. Unfortunately, in general, even in tabular settings, we show that the resulting optimization problem is hard to approximate. On the other hand, motivated by the success of greedy algorithms in classical submodular optimization, we propose SubPO, a simple policy gradient-based algorithm for SubRL that handles non-additive rewards by greedily maximizing marginal gains. Indeed, under some assumptions on the underlying Markov Decision Process (MDP), SubPO recovers optimal constant factor approximations of submodular bandits. Moreover, we derive a natural policy gradient approach for locally optimizing SubRL instances even in large state- and action- spaces. We showcase the versatility of our approach by applying SubPO to several applications, such as biodiversity monitoring, Bayesian experiment design, informative path planning, and coverage maximization. Our results demonstrate sample efficiency, as well as scalability to high-dimensional state-action spaces.

Reinforcement learning (RL), with its ability to explore and optimize policies in complex, dynamic decision-making tasks, has emerged as a promising approach to addressing motion planning (MoP) challenges in autonomous driving (AD). Despite rapid advancements in RL and AD, a systematic description and interpretation of the RL design process tailored to diverse driving tasks remains underdeveloped. This survey provides a comprehensive review of RL-based MoP for AD, focusing on lessons from task-specific perspectives. We first outline the fundamentals of RL methodologies, and then survey their applications in MoP, analyzing scenario-specific features and task requirements to shed light on their influence on RL design choices. Building on this analysis, we summarize key design experiences, extract insights from various driving task applications, and provide guidance for future implementations. Additionally, we examine the frontier challenges in RL-based MoP, review recent efforts to addresse these challenges, and propose strategies for overcoming unresolved issues.

Reward sparsity in long-horizon reinforcement learning (RL) tasks remains a significant challenge, while existing outcome-based reward shaping struggles to define meaningful immediate rewards without introducing bias or requiring explicit task decomposition. Alternatively, verification-based reward shaping uses stepwise critics, but misalignment between immediate rewards and long-term objectives can lead to reward hacking and suboptimal policies. In this work, we address this problem in the context of software engineering (SWE) tasks, where multi-turn reasoning and rule-based verification are critical. We introduce the SWE-oriented RL Framework, a unified system supporting multi-turn interaction, docker-based execution, and customizable reward functions. Additionally, we propose Gated Reward Accumulation (G-RA), a novel method that accumulates immediate rewards only when high-level (long-term) rewards meet a predefined threshold, ensuring stable RL optimization. Experiments on SWE-bench Verified and kBench demonstrate that G-RA leads to an increase in completion rates (47.6\% \rightarrow 93.8\% and 22.0\% \rightarrow 86.0\%) and modification rates (19.6\% \rightarrow 23.8\% and 12.0\% \rightarrow 42.0\%), while avoiding policy degradation caused by reward misalignment. Our findings highlight the importance of balanced reward accumulation in long-horizon RL and provide a practical solution.

A central piece in enabling intelligent agentic behavior in foundation models is to make them capable of introspecting upon their behavior, reasoning, and correcting their mistakes as more computation or interaction is available. Even the strongest proprietary large language models (LLMs) do not quite exhibit the ability of continually improving their responses sequentially, even in scenarios where they are explicitly told that they are making a mistake. In this paper, we develop RISE: Recursive IntroSpEction, an approach for fine-tuning LLMs to introduce this capability, despite prior work hypothesizing that this capability may not be possible to attain. Our approach prescribes an iterative fine-tuning procedure, which attempts to teach the model how to alter its response after having executed previously unsuccessful attempts to solve a hard test-time problem, with optionally additional environment feedback. RISE poses fine-tuning for a single-turn prompt as solving a multi-turn Markov decision process (MDP), where the initial state is the prompt. Inspired by principles in online imitation learning and reinforcement learning, we propose strategies for multi-turn data collection and training so as to imbue an LLM with the capability to recursively detect and correct its previous mistakes in subsequent iterations. Our experiments show that RISE enables Llama2, Llama3, and Mistral models to improve themselves with more turns on math reasoning tasks, outperforming several single-turn strategies given an equal amount of inference-time computation. We also find that RISE scales well, often attaining larger benefits with more capable models. Our analysis shows that RISE makes meaningful improvements to responses to arrive at the correct solution for challenging prompts, without disrupting one-turn abilities as a result of expressing more complex distributions.

With the rapid development of Large Vision Language Models, the focus of Graphical User Interface (GUI) agent tasks shifts from single-screen tasks to complex screen navigation challenges. However, real-world GUI environments, such as PC software and mobile Apps, are often complex and proprietary, making it difficult to obtain the comprehensive environment information needed for agent training and evaluation. This limitation hinders systematic investigation and benchmarking of agent navigation capabilities. To address this limitation, we introduce GUI Exploration Lab, a simulation environment engine for GUI agent navigation research that enables flexible definition and composition of screens, icons, and navigation graphs, while providing full access to environment information for comprehensive agent training and evaluation. Through extensive experiments, we find that supervised fine-tuning enables effective memorization of fundamental knowledge, serving as a crucial foundation for subsequent training. Building on this, single-turn reinforcement learning further enhances generalization to unseen scenarios. Finally, multi-turn reinforcement learning encourages the development of exploration strategies through interactive trial and error, leading to further improvements in screen navigation performance. We validate our methods on both static and interactive benchmarks, demonstrating that our findings generalize effectively to real-world scenarios. These findings demonstrate the advantages of reinforcement learning approaches in GUI navigation and offer practical guidance for building more capable and generalizable GUI agents.

Recent advances in reasoning with large language models (LLMs) have shown the effectiveness of Monte Carlo Tree Search (MCTS) for generating high-quality intermediate trajectories, particularly in math and symbolic domains. Inspired by this, we explore how MCTS-derived trajectories, traditionally used for training value or reward models, can be repurposed to improve policy optimization in preference-based reinforcement learning (RL). Specifically, we focus on Group Relative Policy Optimization (GRPO), a recent algorithm that enables preference-consistent policy learning without value networks. We propose a staged GRPO training paradigm where completions are derived from partially revealed MCTS rollouts, introducing a novel tree-structured setting for advantage estimation. This leads to a rich class of prefix-conditioned reward signals, which we analyze theoretically and empirically. Our initial results indicate that while structured advantage estimation can stabilize updates and better reflect compositional reasoning quality, challenges such as advantage saturation and reward signal collapse remain. We propose heuristic and statistical solutions to mitigate these issues and discuss open challenges for learning under staged or tree-like reward structures.

Collaborative multi-agent reinforcement learning (c-MARL) has rapidly evolved, offering state-of-the-art algorithms for real-world applications, including sensitive domains. However, a key challenge to its widespread adoption is the lack of a thorough investigation into its vulnerabilities to adversarial attacks. Existing work predominantly focuses on training-time attacks or unrealistic scenarios, such as access to policy weights or the ability to train surrogate policies. In this paper, we investigate new vulnerabilities under more realistic and constrained conditions, assuming an adversary can only collect and perturb the observations of deployed agents. We also consider scenarios where the adversary has no access at all. We propose simple yet highly effective algorithms for generating adversarial perturbations designed to misalign how victim agents perceive their environment. Our approach is empirically validated on three benchmarks and 22 environments, demonstrating its effectiveness across diverse algorithms and environments. Furthermore, we show that our algorithm is sample-efficient, requiring only 1,000 samples compared to the millions needed by previous methods.

A prevailing view in Reinforcement Learning for Verifiable Rewards (RLVR) interprets recent progress through the lens of an exploration-exploitation trade-off, a perspective largely shaped by token-level metrics. We re-examine this perspective, proposing that this perceived trade-off may not be a fundamental constraint but rather an artifact of the measurement level. To investigate this, we shift the analysis to the semantically rich hidden-state space, adopting Effective Rank (ER) to quantify exploration and proposing its novel first- and second-order derivatives, named Effective Rank Velocity (ERV) and Effective Rank Acceleration (ERA), to capture exploitation dynamics. Our analysis reveals that at the hidden-state level, exploration and exploitation could be decoupled (Sec. 4). This finding reveals an opportunity to enhance both capacities simultaneously. This insight motivates our method, Velocity-Exploiting Rank-Learning (VERL), the first to operationalize the principle of synergistic exploration-exploitation enhancement by directly shaping the RL advantage function. The key innovation is leveraging the theoretically stable ERA as a predictive meta-controller to create a synergistic, dual-channel incentive structure. Instead of forcing a trade-off, VERL prospectively amplifies rewards for exploration to preempt overconfidence and reinforces exploitative gains to consolidate reasoning. Experiments across diverse LLMs and reasoning benchmarks show consistent gains, including up to 21.4% absolute accuracy improvement on the challenging Gaokao 2024 dataset.

We demonstrate that models trained only in simulation can be used to solve a manipulation problem of unprecedented complexity on a real robot. This is made possible by two key components: a novel algorithm, which we call automatic domain randomization (ADR) and a robot platform built for machine learning. ADR automatically generates a distribution over randomized environments of ever-increasing difficulty. Control policies and vision state estimators trained with ADR exhibit vastly improved sim2real transfer. For control policies, memory-augmented models trained on an ADR-generated distribution of environments show clear signs of emergent meta-learning at test time. The combination of ADR with our custom robot platform allows us to solve a Rubik's cube with a humanoid robot hand, which involves both control and state estimation problems. Videos summarizing our results are available: https://openai.com/blog/solving-rubiks-cube/

One of the fundamental challenges in reinforcement learning (RL) is to take a complex task and be able to decompose it to subtasks that are simpler for the RL agent to learn. In this paper, we report on our work that would identify subtasks by using some given positive and negative trajectories for solving the complex task. We assume that the states are represented by first-order predicate logic using which we devise a novel algorithm to identify the subtasks. Then we employ a Large Language Model (LLM) to generate first-order logic rule templates for achieving each subtask. Such rules were then further fined tuned to a rule-based policy via an Inductive Logic Programming (ILP)-based RL agent. Through experiments, we verify the accuracy of our algorithm in detecting subtasks which successfully detect all of the subtasks correctly. We also investigated the quality of the common-sense rules produced by the language model to achieve the subtasks. Our experiments show that our LLM-guided rule template generation can produce rules that are necessary for solving a subtask, which leads to solving complex tasks with fewer assumptions about predefined first-order logic predicates of the environment.

Policy optimization methods are popular reinforcement learning algorithms in practice. Recent works have built theoretical foundation for them by proving T regret bounds even when the losses are adversarial. Such bounds are tight in the worst case but often overly pessimistic. In this work, we show that in tabular Markov decision processes (MDPs), by properly designing the regularizer, the exploration bonus and the learning rates, one can achieve a more favorable polylog(T) regret when the losses are stochastic, without sacrificing the worst-case guarantee in the adversarial regime. To our knowledge, this is also the first time a gap-dependent polylog(T) regret bound is shown for policy optimization. Specifically, we achieve this by leveraging a Tsallis entropy or a Shannon entropy regularizer in the policy update. Then we show that under known transitions, we can further obtain a first-order regret bound in the adversarial regime by leveraging the log-barrier regularizer.

Recent advancements in LLM-based agents have demonstrated remarkable capabilities in handling complex, knowledge-intensive tasks by integrating external tools. Among diverse choices of tools, search tools play a pivotal role in accessing vast external knowledge. However, open-source agents still fall short of achieving expert-level Search Intelligence, the ability to resolve ambiguous queries, generate precise searches, analyze results, and conduct thorough exploration. Existing approaches fall short in scalability, efficiency, and data quality. For example, small turn limits in existing online RL methods, e.g. <=10, restrict complex strategy learning. This paper introduces ASearcher, an open-source project for large-scale RL training of search agents. Our key contributions include: (1) Scalable fully asynchronous RL training that enables long-horizon search while maintaining high training efficiency. (2) A prompt-based LLM agent that autonomously synthesizes high-quality and challenging QAs, creating a large-scale QA dataset. Through RL training, our prompt-based QwQ-32B agent achieves substantial improvements, with 46.7% and 20.8% Avg@4 gains on xBench and GAIA, respectively. Notably, our agent exhibits extreme long-horizon search, with tool calls exceeding 40 turns and output tokens exceeding 150k during training time. With a simple agent design and no external LLMs, ASearcher-Web-QwQ achieves Avg@4 scores of 42.1 on xBench and 52.8 on GAIA, surpassing existing open-source 32B agents. We open-source our models, training data, and codes in https://github.com/inclusionAI/ASearcher.

Developing autonomous LLM agents capable of making a series of intelligent decisions to solve complex, real-world tasks is a fast-evolving frontier. Like human cognitive development, agents are expected to acquire knowledge and skills through exploration and interaction with the environment. Despite advances, the community still lacks a unified, interactive reinforcement learning (RL) framework that can effectively train such agents from scratch -- without relying on supervised fine-tuning (SFT) -- across diverse and realistic environments. To bridge this gap, we introduce AgentGym-RL, a new framework to train LLM agents for multi-turn interactive decision-making through RL. The framework features a modular and decoupled architecture, ensuring high flexibility and extensibility. It encompasses a wide variety of real-world scenarios, and supports mainstream RL algorithms. Furthermore, we propose ScalingInter-RL, a training approach designed for exploration-exploitation balance and stable RL optimization. In early stages, it emphasizes exploitation by restricting the number of interactions, and gradually shifts towards exploration with larger horizons to encourage diverse problem-solving strategies. In this way, the agent develops more diverse behaviors and is less prone to collapse under long horizons. We perform extensive experiments to validate the stability and effectiveness of both the AgentGym-RL framework and the ScalingInter-RL approach. Our agents match or surpass commercial models on 27 tasks across diverse environments. We offer key insights and will open-source the complete AgentGym-RL framework -- including code and datasets -- to empower the research community in developing the next generation of intelligent agents.

Reinforcement learning (RL) has emerged as a powerful tool for fine-tuning large language models (LLMs) to improve complex reasoning abilities. However, state-of-the-art policy optimization methods often suffer from high computational overhead and memory consumption, primarily due to the need for multiple generations per prompt and the reliance on critic networks or advantage estimates of the current policy. In this paper, we propose A*-PO, a novel two-stage policy optimization framework that directly approximates the optimal advantage function and enables efficient training of LLMs for reasoning tasks. In the first stage, we leverage offline sampling from a reference policy to estimate the optimal value function V*, eliminating the need for costly online value estimation. In the second stage, we perform on-policy updates using a simple least-squares regression loss with only a single generation per prompt. Theoretically, we establish performance guarantees and prove that the KL-regularized RL objective can be optimized without requiring complex exploration strategies. Empirically, A*-PO achieves competitive performance across a wide range of mathematical reasoning benchmarks, while reducing training time by up to 2times and peak memory usage by over 30% compared to PPO, GRPO, and REBEL. Implementation of A*-PO can be found at https://github.com/ZhaolinGao/A-PO.

Large language model (LLM) agents need to perform multi-turn interactions in real-world tasks. However, existing multi-turn RL algorithms for optimizing LLM agents fail to perform effective credit assignment over multiple turns while leveraging the generalization capabilities of LLMs and it remains unclear how to develop such algorithms. To study this, we first introduce a new benchmark, ColBench, where an LLM agent interacts with a human collaborator over multiple turns to solve realistic tasks in backend programming and frontend design. Building on this benchmark, we propose a novel RL algorithm, SWEET-RL (RL with Step-WisE Evaluation from Training-time information), that uses a carefully designed optimization objective to train a critic model with access to additional training-time information. The critic provides step-level rewards for improving the policy model. Our experiments demonstrate that SWEET-RL achieves a 6% absolute improvement in success and win rates on ColBench compared to other state-of-the-art multi-turn RL algorithms, enabling Llama-3.1-8B to match or exceed the performance of GPT4-o in realistic collaborative content creation.

We investigate reinforcement learning (RL) for privileged planning in autonomous driving. State-of-the-art approaches for this task are rule-based, but these methods do not scale to the long tail. RL, on the other hand, is scalable and does not suffer from compounding errors like imitation learning. Contemporary RL approaches for driving use complex shaped rewards that sum multiple individual rewards, \eg~progress, position, or orientation rewards. We show that PPO fails to optimize a popular version of these rewards when the mini-batch size is increased, which limits the scalability of these approaches. Instead, we propose a new reward design based primarily on optimizing a single intuitive reward term: route completion. Infractions are penalized by terminating the episode or multiplicatively reducing route completion. We find that PPO scales well with higher mini-batch sizes when trained with our simple reward, even improving performance. Training with large mini-batch sizes enables efficient scaling via distributed data parallelism. We scale PPO to 300M samples in CARLA and 500M samples in nuPlan with a single 8-GPU node. The resulting model achieves 64 DS on the CARLA longest6 v2 benchmark, outperforming other RL methods with more complex rewards by a large margin. Requiring only minimal adaptations from its use in CARLA, the same method is the best learning-based approach on nuPlan. It scores 91.3 in non-reactive and 90.6 in reactive traffic on the Val14 benchmark while being an order of magnitude faster than prior work.

Compositional reinforcement learning is a promising approach for training policies to perform complex long-horizon tasks. Typically, a high-level task is decomposed into a sequence of subtasks and a separate policy is trained to perform each subtask. In this paper, we focus on the problem of training subtask policies in a way that they can be used to perform any task; here, a task is given by a sequence of subtasks. We aim to maximize the worst-case performance over all tasks as opposed to the average-case performance. We formulate the problem as a two agent zero-sum game in which the adversary picks the sequence of subtasks. We propose two RL algorithms to solve this game: one is an adaptation of existing multi-agent RL algorithms to our setting and the other is an asynchronous version which enables parallel training of subtask policies. We evaluate our approach on two multi-task environments with continuous states and actions and demonstrate that our algorithms outperform state-of-the-art baselines.

The integration of Large Language Models (LLMs) into automated theorem proving has shown immense promise, yet is fundamentally constrained by challenges in scaling up both training-time reinforcement learning (RL) and inference-time compute. This paper introduces BFS-Prover-V2, a system designed to address this dual scaling problem. We present two primary innovations. The first is a novel multi-turn off-policy RL framework for continually improving the performance of LLM step-prover at training time. This framework, inspired by the principles of AlphaZero, utilizes a multi-stage expert iteration pipeline featuring adaptive tactic-level data filtering and periodic retraining to surmount the performance plateaus that typically curtail long-term RL in LLM-based agents. The second innovation is a planner-enhanced multi-agent search architecture that scales reasoning capabilities at inference time. This architecture employs a general reasoning model as a high-level planner to iteratively decompose complex theorems into a sequence of simpler subgoals. This hierarchical approach substantially reduces the search space, enabling a team of parallel prover agents to collaborate efficiently by leveraging a shared proof cache. We demonstrate that this dual approach to scaling yields state-of-the-art results on established formal mathematics benchmarks. BFS-Prover-V2 achieves 95.08\% and 41.4\% on the MiniF2F and ProofNet test sets respectively. While demonstrated in the domain of formal mathematics, the RL and inference techniques presented in this work are of broader interest and may be applied to other domains requiring long-horizon multi-turn reasoning and complex search.

Recent advances in large language models (LLMs) have sparked growing interest in building generalist agents that can learn through online interactions. However, applying reinforcement learning (RL) to train LLM agents in multi-turn, multi-task settings remains challenging due to lack of scalable infrastructure and stable training algorithms. In this work, we present the AgentRL framework for scalable multi-turn, multi-task agentic RL training. On the infrastructure side, AgentRL features a fully-asynchronous generation-training pipeline for efficient multi-turn RL. To support heterogeneous environment development in multi-task RL, we design a unified function-call based API interface, containerized environment development, and a centralized controller. On the algorithm side, we propose cross-policy sampling to encourage model exploration in multi-turn settings and task advantage normalization to stabilize multi-task training. Experiments show that AgentRL, trained on open LLMs across five agentic tasks, significantly outperforms GPT-5, Clause-Sonnet-4, DeepSeek-R1, and other open-source LLM agents. Multi-task training with AgentRL matches the best results among all task-specific models. AgentRL is open-sourced at https://github.com/THUDM/AgentRL. The algorithm and framework are adopted in building \href{https://autoglm.zhipuai.cn{AutoGLM}}.

Despite recent advances in improving the sample-efficiency of reinforcement learning (RL) algorithms, designing an RL algorithm that can be practically deployed in real-world environments remains a challenge. In this paper, we present Coarse-to-fine Reinforcement Learning (CRL), a framework that trains RL agents to zoom-into a continuous action space in a coarse-to-fine manner, enabling the use of stable, sample-efficient value-based RL algorithms for fine-grained continuous control tasks. Our key idea is to train agents that output actions by iterating the procedure of (i) discretizing the continuous action space into multiple intervals and (ii) selecting the interval with the highest Q-value to further discretize at the next level. We then introduce a concrete, value-based algorithm within the CRL framework called Coarse-to-fine Q-Network (CQN). Our experiments demonstrate that CQN significantly outperforms RL and behavior cloning baselines on 20 sparsely-rewarded RLBench manipulation tasks with a modest number of environment interactions and expert demonstrations. We also show that CQN robustly learns to solve real-world manipulation tasks within a few minutes of online training.

Recently, the emergence of agentic RL has showcased that RL could also effectively improve the agentic reasoning ability of LLMs, yet the key design principles and optimal practices remain unclear. In this work, we conduct a comprehensive and systematic investigation to demystify reinforcement learning in agentic reasoning from three key perspectives: data, algorithm, and reasoning mode. We highlight our key insights: (i) Replacing stitched synthetic trajectories with real end-to-end tool-use trajectories yields a far stronger SFT initialization; high-diversity, model-aware datasets sustain exploration and markedly improve RL performance. (ii) Exploration-friendly techniques are crucial for agentic RL, such as clip higher, overlong reward shaping, and maintaining adequate policy entropy could improve the training efficiency. (iii) A deliberative strategy with fewer tool calls outperforms frequent tool calls or verbose self-reasoning, improving tool efficiency and final accuracy. Together, these simple practices consistently enhance agentic reasoning and training efficiency, achieving strong results on challenging benchmarks with smaller models, and establishing a practical baseline for future agentic RL research. Beyond these empirical insights, we further contribute a high-quality, real end-to-end agentic SFT dataset along with a high-quality RL dataset, and demonstrate the effectiveness of our insights in boosting the agentic reasoning ability of LLMs across four challenging benchmarks, including AIME2024/AIME2025, GPQA-Diamond, and LiveCodeBench-v6. With our recipes, 4B-sized models could also achieve superior agentic reasoning performance compared to 32B-sized models. Code and models: https://github.com/Gen-Verse/Open-AgentRL

We study infinite-horizon average-reward Markov decision processes (AMDPs) in the context of general function approximation. Specifically, we propose a novel algorithmic framework named Local-fitted Optimization with OPtimism (LOOP), which incorporates both model-based and value-based incarnations. In particular, LOOP features a novel construction of confidence sets and a low-switching policy updating scheme, which are tailored to the average-reward and function approximation setting. Moreover, for AMDPs, we propose a novel complexity measure -- average-reward generalized eluder coefficient (AGEC) -- which captures the challenge of exploration in AMDPs with general function approximation. Such a complexity measure encompasses almost all previously known tractable AMDP models, such as linear AMDPs and linear mixture AMDPs, and also includes newly identified cases such as kernel AMDPs and AMDPs with Bellman eluder dimensions. Using AGEC, we prove that LOOP achieves a sublinear mathcal{O}(poly(d, sp(V^*)) Tbeta ) regret, where d and beta correspond to AGEC and log-covering number of the hypothesis class respectively, sp(V^*) is the span of the optimal state bias function, T denotes the number of steps, and mathcal{O} (cdot) omits logarithmic factors. When specialized to concrete AMDP models, our regret bounds are comparable to those established by the existing algorithms designed specifically for these special cases. To the best of our knowledge, this paper presents the first comprehensive theoretical framework capable of handling nearly all AMDPs.

Real-world robotic manipulation in homes and factories demands reliability, efficiency, and robustness that approach or surpass skilled human operators. We present RL-100, a real-world reinforcement learning training framework built on diffusion visuomotor policies trained bu supervised learning. RL-100 introduces a three-stage pipeline. First, imitation learning leverages human priors. Second, iterative offline reinforcement learning uses an Offline Policy Evaluation procedure, abbreviated OPE, to gate PPO-style updates that are applied in the denoising process for conservative and reliable improvement. Third, online reinforcement learning eliminates residual failure modes. An additional lightweight consistency distillation head compresses the multi-step sampling process in diffusion into a single-step policy, enabling high-frequency control with an order-of-magnitude reduction in latency while preserving task performance. The framework is task-, embodiment-, and representation-agnostic and supports both 3D point clouds and 2D RGB inputs, a variety of robot platforms, and both single-step and action-chunk policies. We evaluate RL-100 on seven real-robot tasks spanning dynamic rigid-body control, such as Push-T and Agile Bowling, fluids and granular pouring, deformable cloth folding, precise dexterous unscrewing, and multi-stage orange juicing. RL-100 attains 100\% success across evaluated trials for a total of 900 out of 900 episodes, including up to 250 out of 250 consecutive trials on one task. The method achieves near-human teleoperation or better time efficiency and demonstrates multi-hour robustness with uninterrupted operation lasting up to two hours.

Current advancements in reinforcement learning (RL) have predominantly focused on learning step-based policies that generate actions for each perceived state. While these methods efficiently leverage step information from environmental interaction, they often ignore the temporal correlation between actions, resulting in inefficient exploration and unsmooth trajectories that are challenging to implement on real hardware. Episodic RL (ERL) seeks to overcome these challenges by exploring in parameters space that capture the correlation of actions. However, these approaches typically compromise data efficiency, as they treat trajectories as opaque black boxes. In this work, we introduce a novel ERL algorithm, Temporally-Correlated Episodic RL (TCE), which effectively utilizes step information in episodic policy updates, opening the 'black box' in existing ERL methods while retaining the smooth and consistent exploration in parameter space. TCE synergistically combines the advantages of step-based and episodic RL, achieving comparable performance to recent ERL methods while maintaining data efficiency akin to state-of-the-art (SoTA) step-based RL.

We propose a method for meta-learning reinforcement learning algorithms by searching over the space of computational graphs which compute the loss function for a value-based model-free RL agent to optimize. The learned algorithms are domain-agnostic and can generalize to new environments not seen during training. Our method can both learn from scratch and bootstrap off known existing algorithms, like DQN, enabling interpretable modifications which improve performance. Learning from scratch on simple classical control and gridworld tasks, our method rediscovers the temporal-difference (TD) algorithm. Bootstrapped from DQN, we highlight two learned algorithms which obtain good generalization performance over other classical control tasks, gridworld type tasks, and Atari games. The analysis of the learned algorithm behavior shows resemblance to recently proposed RL algorithms that address overestimation in value-based methods.

Large Language Models (LLMs) often struggle with problems that require multi-step reasoning. For small-scale open-source models, Reinforcement Learning with Verifiable Rewards (RLVR) fails when correct solutions are rarely sampled even after many attempts, while Supervised Fine-Tuning (SFT) tends to overfit long demonstrations through rigid token-by-token imitation. To address this gap, we propose Supervised Reinforcement Learning (SRL), a framework that reformulates problem solving as generating a sequence of logical "actions". SRL trains the model to generate an internal reasoning monologue before committing to each action. It provides smoother rewards based on the similarity between the model's actions and expert actions extracted from the SFT dataset in a step-wise manner. This supervision offers richer learning signals even when all rollouts are incorrect, while encouraging flexible reasoning guided by expert demonstrations. As a result, SRL enables small models to learn challenging problems previously unlearnable by SFT or RLVR. Moreover, initializing training with SRL before refining with RLVR yields the strongest overall performance. Beyond reasoning benchmarks, SRL generalizes effectively to agentic software engineering tasks, establishing it as a robust and versatile training framework for reasoning-oriented LLMs.

Reinforcement learning (RL) for continuous control often requires large amounts of online interaction data. Value-based RL methods can mitigate this burden by offering relatively high sample efficiency. Some studies further enhance sample efficiency by incorporating offline demonstration data to "kick-start" training, achieving promising results in continuous control. However, they typically compute the Q-function independently for each action dimension, neglecting interdependencies and making it harder to identify optimal actions when learning from suboptimal data, such as non-expert demonstration and online-collected data during the training process. To address these issues, we propose Auto-Regressive Soft Q-learning (ARSQ), a value-based RL algorithm that models Q-values in a coarse-to-fine, auto-regressive manner. First, ARSQ decomposes the continuous action space into discrete spaces in a coarse-to-fine hierarchy, enhancing sample efficiency for fine-grained continuous control tasks. Next, it auto-regressively predicts dimensional action advantages within each decision step, enabling more effective decision-making in continuous control tasks. We evaluate ARSQ on two continuous control benchmarks, RLBench and D4RL, integrating demonstration data into online training. On D4RL, which includes non-expert demonstrations, ARSQ achieves an average 1.62times performance improvement over SOTA value-based baseline. On RLBench, which incorporates expert demonstrations, ARSQ surpasses various baselines, demonstrating its effectiveness in learning from suboptimal online-collected data. Project page is at https://sites.google.com/view/ar-soft-q

Discrete-action reinforcement learning algorithms often falter in tasks with high-dimensional discrete action spaces due to the vast number of possible actions. A recent advancement leverages value-decomposition, a concept from multi-agent reinforcement learning, to tackle this challenge. This study delves deep into the effects of this value-decomposition, revealing that whilst it curtails the over-estimation bias inherent to Q-learning algorithms, it amplifies target variance. To counteract this, we present an ensemble of critics to mitigate target variance. Moreover, we introduce a regularisation loss that helps to mitigate the effects that exploratory actions in one dimension can have on the value of optimal actions in other dimensions. Our novel algorithm, REValueD, tested on discretised versions of the DeepMind Control Suite tasks, showcases superior performance, especially in the challenging humanoid and dog tasks. We further dissect the factors influencing REValueD's performance, evaluating the significance of the regularisation loss and the scalability of REValueD with increasing sub-actions per dimension.

Reinforcement learning (RL) promises a framework for near-universal problem-solving. In practice however, RL algorithms are often tailored to specific benchmarks, relying on carefully tuned hyperparameters and algorithmic choices. Recently, powerful model-based RL methods have shown impressive general results across benchmarks but come at the cost of increased complexity and slow run times, limiting their broader applicability. In this paper, we attempt to find a unifying model-free deep RL algorithm that can address a diverse class of domains and problem settings. To achieve this, we leverage model-based representations that approximately linearize the value function, taking advantage of the denser task objectives used by model-based RL while avoiding the costs associated with planning or simulated trajectories. We evaluate our algorithm, MR.Q, on a variety of common RL benchmarks with a single set of hyperparameters and show a competitive performance against domain-specific and general baselines, providing a concrete step towards building general-purpose model-free deep RL algorithms.

End-to-end autonomous driving has emerged as a promising paradigm for directly mapping sensor inputs to planning maneuvers using learning-based modular integrations. However, existing imitation learning (IL)-based models suffer from generalization to hard cases, and a lack of corrective feedback loop under post-deployment. While reinforcement learning (RL) offers a potential solution to tackle hard cases with optimality, it is often hindered by overfitting to specific driving cases, resulting in catastrophic forgetting of generalizable knowledge and sample inefficiency. To overcome these challenges, we propose Reinforced Refinement with Self-aware Expansion (R2SE), a novel learning pipeline that constantly refines hard domain while keeping generalizable driving policy for model-agnostic end-to-end driving systems. Through reinforcement fine-tuning and policy expansion that facilitates continuous improvement, R2SE features three key components: 1) Generalist Pretraining with hard-case allocation trains a generalist imitation learning (IL) driving system while dynamically identifying failure-prone cases for targeted refinement; 2) Residual Reinforced Specialist Fine-tuning optimizes residual corrections using reinforcement learning (RL) to improve performance in hard case domain while preserving global driving knowledge; 3) Self-aware Adapter Expansion dynamically integrates specialist policies back into the generalist model, enhancing continuous performance improvement. Experimental results in closed-loop simulation and real-world datasets demonstrate improvements in generalization, safety, and long-horizon policy robustness over state-of-the-art E2E systems, highlighting the effectiveness of reinforce refinement for scalable autonomous driving.

Robustness against adversarial attacks and distribution shifts is a long-standing goal of Reinforcement Learning (RL). To this end, Robust Adversarial Reinforcement Learning (RARL) trains a protagonist against destabilizing forces exercised by an adversary in a competitive zero-sum Markov game, whose optimal solution, i.e., rational strategy, corresponds to a Nash equilibrium. However, finding Nash equilibria requires facing complex saddle point optimization problems, which can be prohibitive to solve, especially for high-dimensional control. In this paper, we propose a novel approach for adversarial RL based on entropy regularization to ease the complexity of the saddle point optimization problem. We show that the solution of this entropy-regularized problem corresponds to a Quantal Response Equilibrium (QRE), a generalization of Nash equilibria that accounts for bounded rationality, i.e., agents sometimes play random actions instead of optimal ones. Crucially, the connection between the entropy-regularized objective and QRE enables free modulation of the rationality of the agents by simply tuning the temperature coefficient. We leverage this insight to propose our novel algorithm, Quantal Adversarial RL (QARL), which gradually increases the rationality of the adversary in a curriculum fashion until it is fully rational, easing the complexity of the optimization problem while retaining robustness. We provide extensive evidence of QARL outperforming RARL and recent baselines across several MuJoCo locomotion and navigation problems in overall performance and robustness.

Sequential decision-making agents struggle with long horizon tasks, since solving them requires multi-step reasoning. Most reinforcement learning (RL) algorithms address this challenge by improved credit assignment, introducing memory capability, altering the agent's intrinsic motivation (i.e. exploration) or its worldview (i.e. knowledge representation). Many of these components could be learned from offline data. In this work, we follow the hypothesis that exploration and representation learning can be improved by separately learning two different models from a single offline dataset. We show that learning a state representation using noise-contrastive estimation and a model of auxiliary reward separately from a single collection of human demonstrations can significantly improve the sample efficiency on the challenging NetHack benchmark. We also ablate various components of our experimental setting and highlight crucial insights.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a powerful paradigm for facilitating the self-improvement of large language models (LLMs), particularly in the domain of complex reasoning tasks. However, prevailing on-policy RL methods often contend with significant training instability and inefficiency. This is primarily due to a capacity-difficulty mismatch, where the complexity of training data frequently outpaces the model's current capabilities, leading to critically sparse reward signals and stalled learning progress. This challenge is particularly acute for smaller, more resource-efficient LLMs. To overcome this, we introduce the Guided Hybrid Policy Optimization (GHPO), a novel difficulty-aware reinforcement learning framework. GHPO dynamically calibrates task difficulty by employing adaptive prompt refinement to provide targeted guidance. This unique approach adaptively balances direct imitation learning for problems currently beyond the model's reach with exploration-based reinforcement learning for more manageable tasks, effectively creating a smooth and optimized learning curriculum. Extensive experiments demonstrate that GHPO achieves an average performance gain of approximately 5% across six challenging mathematics benchmarks, consistently outperforming strong on-policy reinforcement learning and curriculum learning baselines. Further analysis confirms that our framework significantly enhances both training stability and final reasoning performance, thus offering a scalable and efficient solution for developing powerful and robust reasoning models.

For continuous action spaces, actor-critic methods are widely used in online reinforcement learning (RL). However, unlike RL algorithms for discrete actions, which generally model the optimal value function using the Bellman optimality operator, RL algorithms for continuous actions typically model Q-values for the current policy using the Bellman operator. These algorithms for continuous actions rely exclusively on policy updates for improvement, which often results in low sample efficiency. This study examines the effectiveness of incorporating the Bellman optimality operator into actor-critic frameworks. Experiments in a simple environment show that modeling optimal values accelerates learning but leads to overestimation bias. To address this, we propose an annealing approach that gradually transitions from the Bellman optimality operator to the Bellman operator, thereby accelerating learning while mitigating bias. Our method, combined with TD3 and SAC, significantly outperforms existing approaches across various locomotion and manipulation tasks, demonstrating improved performance and robustness to hyperparameters related to optimality. The code for this study is available at https://github.com/motokiomura/annealed-q-learning.

Latent prediction--where agents learn by predicting their own latents--has emerged as a powerful paradigm for training general representations in machine learning. In reinforcement learning (RL), this approach has been explored to define auxiliary losses for a variety of settings, including reward-based and unsupervised RL, behavior cloning, and world modeling. While existing methods are typically limited to single-task learning, one-step prediction, or on-policy trajectory data, we show that temporal difference (TD) learning enables learning representations predictive of long-term latent dynamics across multiple policies from offline, reward-free transitions. Building on this, we introduce TD-JEPA, which leverages TD-based latent-predictive representations into unsupervised RL. TD-JEPA trains explicit state and task encoders, a policy-conditioned multi-step predictor, and a set of parameterized policies directly in latent space. This enables zero-shot optimization of any reward function at test time. Theoretically, we show that an idealized variant of TD-JEPA avoids collapse with proper initialization, and learns encoders that capture a low-rank factorization of long-term policy dynamics, while the predictor recovers their successor features in latent space. Empirically, TD-JEPA matches or outperforms state-of-the-art baselines on locomotion, navigation, and manipulation tasks across 13 datasets in ExoRL and OGBench, especially in the challenging setting of zero-shot RL from pixels.

Recent advancements in post-training methodologies for large language models (LLMs) have highlighted reinforcement learning (RL) as a critical component for enhancing reasoning. However, the substantial computational costs associated with RL-based approaches have led to growing interest in alternative paradigms, such as Direct Preference Optimization (DPO). In this study, we investigate the effectiveness of DPO in facilitating self-improvement for LLMs through iterative preference-based learning. We demonstrate that a single round of DPO with coarse filtering significantly enhances mathematical reasoning performance, particularly for strong base model. Furthermore, we design an iterative enhancement framework for both the generator and the reward model (RM), enabling their mutual improvement through online interaction across multiple rounds of DPO. Finally, with simple verifiable rewards, our model DPO-VP achieves RL-level performance with significantly lower computational overhead. These findings highlight DPO as a scalable and cost-effective alternative to RL, offering a practical solution for enhancing LLM reasoning in resource-constrained situations.

Recent studies have shown the great potential of diffusion models in improving reinforcement learning (RL) by modeling complex policies, expressing a high degree of multi-modality, and efficiently handling high-dimensional continuous control tasks. However, there is currently limited research on how to optimize diffusion-based polices (e.g., Diffusion Policy) fast and stably. In this paper, we propose an Adam-based Diffusion Policy Optimization (ADPO), a fast algorithmic framework containing best practices for fine-tuning diffusion-based polices in robotic control tasks using the adaptive gradient descent method in RL. Adaptive gradient method is less studied in training RL, let alone diffusion-based policies. We confirm that ADPO outperforms other diffusion-based RL methods in terms of overall effectiveness for fine-tuning on standard robotic tasks. Concretely, we conduct extensive experiments on standard robotic control tasks to test ADPO, where, particularly, six popular diffusion-based RL methods are provided as benchmark methods. Experimental results show that ADPO acquires better or comparable performance than the baseline methods. Finally, we systematically analyze the sensitivity of multiple hyperparameters in standard robotics tasks, providing guidance for subsequent practical applications. Our video demonstrations are released in https://github.com/Timeless-lab/ADPO.git.

Critic-free methods like GRPO reduce memory demands by estimating advantages from multiple rollouts but tend to converge slowly, as critical learning signals are diluted by an abundance of uninformative samples and tokens. To tackle this challenge, we propose the Dynamic Dual-Level Down-Sampling (D^3S) framework that prioritizes the most informative samples and tokens across groups to improve the efficient of policy optimization. D^3S operates along two levels: (1) the sample-level, which selects a subset of rollouts to maximize advantage variance (Var(A)). We theoretically proven that this selection is positively correlated with the upper bound of the policy gradient norms, yielding higher policy gradients. (2) the token-level, which prioritizes tokens with a high product of advantage magnitude and policy entropy (|A_{i,t}|times H_{i,t}), focusing updates on tokens where the policy is both uncertain and impactful. Moreover, to prevent overfitting to high-signal data, D^3S employs a dynamic down-sampling schedule inspired by curriculum learning. This schedule starts with aggressive down-sampling to accelerate early learning and gradually relaxes to promote robust generalization. Extensive experiments on Qwen2.5 and Llama3.1 demonstrate that integrating D^3S into advanced RL algorithms achieves state-of-the-art performance and generalization while requiring fewer samples and tokens across diverse reasoning benchmarks. Our code is added in the supplementary materials and will be made publicly available.

The study of provable adversarial robustness for deep neural networks (DNNs) has mainly focused on static supervised learning tasks such as image classification. However, DNNs have been used extensively in real-world adaptive tasks such as reinforcement learning (RL), making such systems vulnerable to adversarial attacks as well. Prior works in provable robustness in RL seek to certify the behaviour of the victim policy at every time-step against a non-adaptive adversary using methods developed for the static setting. But in the real world, an RL adversary can infer the defense strategy used by the victim agent by observing the states, actions, etc., from previous time-steps and adapt itself to produce stronger attacks in future steps. We present an efficient procedure, designed specifically to defend against an adaptive RL adversary, that can directly certify the total reward without requiring the policy to be robust at each time-step. Our main theoretical contribution is to prove an adaptive version of the Neyman-Pearson Lemma -- a key lemma for smoothing-based certificates -- where the adversarial perturbation at a particular time can be a stochastic function of current and previous observations and states as well as previous actions. Building on this result, we propose policy smoothing where the agent adds a Gaussian noise to its observation at each time-step before passing it through the policy function. Our robustness certificates guarantee that the final total reward obtained by policy smoothing remains above a certain threshold, even though the actions at intermediate time-steps may change under the attack. Our experiments on various environments like Cartpole, Pong, Freeway and Mountain Car show that our method can yield meaningful robustness guarantees in practice.

The goal of reinforcement learning (RL) is to find a policy that maximizes the expected cumulative return. It has been shown that this objective can be represented as an optimization problem of state-action visitation distribution under linear constraints. The dual problem of this formulation, which we refer to as dual RL, is unconstrained and easier to optimize. In this work, we first cast several state-of-the-art offline RL and offline imitation learning (IL) algorithms as instances of dual RL approaches with shared structures. Such unification allows us to identify the root cause of the shortcomings of prior methods. For offline IL, our analysis shows that prior methods are based on a restrictive coverage assumption that greatly limits their performance in practice. To fix this limitation, we propose a new discriminator-free method ReCOIL that learns to imitate from arbitrary off-policy data to obtain near-expert performance. For offline RL, our analysis frames a recent offline RL method XQL in the dual framework, and we further propose a new method f-DVL that provides alternative choices to the Gumbel regression loss that fixes the known training instability issue of XQL. The performance improvements by both of our proposed methods, ReCOIL and f-DVL, in IL and RL are validated on an extensive suite of simulated robot locomotion and manipulation tasks. Project code and details can be found at this https://hari-sikchi.github.io/dual-rl.

As autonomous agents become adept at understanding and interacting with graphical user interface (GUI) environments, a new era of automated task execution is emerging. Recent studies have demonstrated that Reinforcement Learning (RL) can effectively enhance agents' performance in dynamic interactive GUI environments. However, these methods face two key limitations: (1) they overlook the significant variation in difficulty across different GUI tasks by treating the entire training data as a uniform set, which hampers the agent's ability to adapt its learning process; and (2) most approaches collapse task-specific nuances into a single, coarse reward, leaving the agent with a uniform signal that yields inefficient policy updates. To address these limitations, we propose CRAFT-GUI, a curriculum learning framework based on Group Relative Policy Optimization (GRPO) that explicitly accounts for the varying difficulty across trajectories. To enable more fine-grained policy optimization, we design a reward function that combines simple rule-based signals with model-judged evaluation, providing richer and more nuanced feedback during training. Experimental results demonstrate that our method achieves significant improvements over previous state-of-the-art approaches, outperforming them by 5.6% on public benchmarks Android Control and 10.3% on our internal online benchmarks, respectively. These findings empirically validate the effectiveness of integrating reinforcement learning with curriculum learning in GUI interaction tasks.

Augmenting large language models (LLMs) with browsing tools substantially improves their potential as deep search agents to solve complex, real-world tasks. Yet, open LLMs still perform poorly in such settings due to limited long-horizon reasoning capacity with browsing tools and the lack of sufficiently difficult supervised data. To address these challenges, we present DeepDive to advance deep search agents. First, we propose a strategy to automatically synthesize complex, difficult, and hard-to-find questions from open knowledge graphs. Second, we apply end-to-end multi-turn reinforcement learning (RL) to enhance LLMs' long-horizon reasoning with deep search. Experiments show that DeepDive-32B achieves a new open-source competitive result on BrowseComp, outperforming WebSailor, DeepSeek-R1-Browse, and Search-o1. We demonstrate that multi-turn RL training improves deep search ability and significantly contributes to the performance improvements across multiple benchmarks. We observe that DeepDive enables test-time scaling of tool calls and parallel sampling. All datasets, models, and code are publicly available at https://github.com/THUDM/DeepDive.

Recent studies have shown that episodic reinforcement learning (RL) is no harder than bandits when the total reward is bounded by 1, and proved regret bounds that have a polylogarithmic dependence on the planning horizon H. However, it remains an open question that if such results can be carried over to adversarial RL, where the reward is adversarially chosen at each episode. In this paper, we answer this question affirmatively by proposing the first horizon-free policy search algorithm. To tackle the challenges caused by exploration and adversarially chosen reward, our algorithm employs (1) a variance-uncertainty-aware weighted least square estimator for the transition kernel; and (2) an occupancy measure-based technique for the online search of a stochastic policy. We show that our algorithm achieves an Obig((d+log (|S|^2 |A|))Kbig) regret with full-information feedback, where d is the dimension of a known feature mapping linearly parametrizing the unknown transition kernel of the MDP, K is the number of episodes, |S| and |A| are the cardinalities of the state and action spaces. We also provide hardness results and regret lower bounds to justify the near optimality of our algorithm and the unavoidability of log|S| and log|A| in the regret bound.

Recently, data augmentation (DA) has emerged as a method for leveraging domain knowledge to inexpensively generate additional data in reinforcement learning (RL) tasks, often yielding substantial improvements in data efficiency. While prior work has demonstrated the utility of incorporating augmented data directly into model-free RL updates, it is not well-understood when a particular DA strategy will improve data efficiency. In this paper, we seek to identify general aspects of DA responsible for observed learning improvements. Our study focuses on sparse-reward tasks with dynamics-invariant data augmentation functions, serving as an initial step towards a more general understanding of DA and its integration into RL training. Experimentally, we isolate three relevant aspects of DA: state-action coverage, reward density, and the number of augmented transitions generated per update (the augmented replay ratio). From our experiments, we draw two conclusions: (1) increasing state-action coverage often has a much greater impact on data efficiency than increasing reward density, and (2) decreasing the augmented replay ratio substantially improves data efficiency. In fact, certain tasks in our empirical study are solvable only when the replay ratio is sufficiently low.

Reinforcement learning (RL) holds significant promise for training LLM agents to handle complex, goal-oriented tasks that require multi-step interactions with external environments. However, a critical challenge when applying RL to these agentic tasks arises from delayed rewards: feedback signals are typically available only after the entire task is completed. This makes it non-trivial to assign delayed rewards to earlier actions, providing insufficient guidance regarding environmental constraints and hindering agent training. In this work, we draw on the insight that the ultimate completion of a task emerges from the cumulative progress an agent makes across individual steps. We propose Stepwise Progress Attribution (SPA), a general reward redistribution framework that decomposes the final reward into stepwise contributions, each reflecting its incremental progress toward overall task completion. To achieve this, we train a progress estimator that accumulates stepwise contributions over a trajectory to match the task completion. During policy optimization, we combine the estimated per-step contribution with a grounding signal for actions executed in the environment as the fine-grained, intermediate reward for effective agent training. Extensive experiments on common agent benchmarks (including Webshop, ALFWorld, and VirtualHome) demonstrate that SPA consistently outperforms the state-of-the-art method in both success rate (+2.5\% on average) and grounding accuracy (+1.9\% on average). Further analyses demonstrate that our method remarkably provides more effective intermediate rewards for RL training. Our code is available at https://github.com/WangHanLinHenry/SPA-RL-Agent.

Deep reinforcement learning (RL) can enable robots to autonomously acquire complex behaviors, such as legged locomotion. However, RL in the real world is complicated by constraints on efficiency, safety, and overall training stability, which limits its practical applicability. We present APRL, a policy regularization framework that modulates the robot's exploration over the course of training, striking a balance between flexible improvement potential and focused, efficient exploration. APRL enables a quadrupedal robot to efficiently learn to walk entirely in the real world within minutes and continue to improve with more training where prior work saturates in performance. We demonstrate that continued training with APRL results in a policy that is substantially more capable of navigating challenging situations and is able to adapt to changes in dynamics with continued training.

Recent studies generally enhance MLLMs' reasoning capabilities via supervised fine-tuning on high-quality chain-of-thought reasoning data, which often leads models to merely imitate successful reasoning paths without understanding what the wrong reasoning paths are. In this work, we aim to enhance the MLLMs' reasoning ability beyond passively imitating positive reasoning paths. To this end, we design Step-wise Group Relative Policy Optimization (StepGRPO), a new online reinforcement learning framework that enables MLLMs to self-improve reasoning ability via simple, effective and dense step-wise rewarding. Specifically, StepGRPO introduces two novel rule-based reasoning rewards: Step-wise Reasoning Accuracy Reward (StepRAR) and Step-wise Reasoning Validity Reward (StepRVR). StepRAR rewards the reasoning paths that contain necessary intermediate reasoning steps via a soft key-step matching technique, while StepRAR rewards reasoning paths that follow a well-structured and logically consistent reasoning process through a reasoning completeness and logic evaluation strategy. With the proposed StepGRPO, we introduce R1-VL, a series of MLLMs with outstanding capabilities in step-by-step reasoning. Extensive experiments over 8 benchmarks demonstrate the superiority of our methods.

Deep Generative AI has been a long-standing essential topic in the machine learning community, which can impact a number of application areas like text generation and computer vision. The major paradigm to train a generative model is maximum likelihood estimation, which pushes the learner to capture and approximate the target data distribution by decreasing the divergence between the model distribution and the target distribution. This formulation successfully establishes the objective of generative tasks, while it is incapable of satisfying all the requirements that a user might expect from a generative model. Reinforcement learning, serving as a competitive option to inject new training signals by creating new objectives that exploit novel signals, has demonstrated its power and flexibility to incorporate human inductive bias from multiple angles, such as adversarial learning, hand-designed rules and learned reward model to build a performant model. Thereby, reinforcement learning has become a trending research field and has stretched the limits of generative AI in both model design and application. It is reasonable to summarize and conclude advances in recent years with a comprehensive review. Although there are surveys in different application areas recently, this survey aims to shed light on a high-level review that spans a range of application areas. We provide a rigorous taxonomy in this area and make sufficient coverage on various models and applications. Notably, we also surveyed the fast-developing large language model area. We conclude this survey by showing the potential directions that might tackle the limit of current models and expand the frontiers for generative AI.

The Vision-and-Language Navigation (VLN) task requires an agent to follow natural language instructions and navigate through complex environments. Existing MLLM-based VLN methods primarily rely on imitation learning (IL) and often use DAgger for post-training to mitigate covariate shift. While effective, these approaches incur substantial data collection and training costs. Reinforcement learning (RL) offers a promising alternative. However, prior VLN RL methods lack dynamic interaction with the environment and depend on expert trajectories for reward shaping, rather than engaging in open-ended active exploration. This restricts the agent's ability to discover diverse and plausible navigation routes. To address these limitations, we propose ActiveVLN, a VLN framework that explicitly enables active exploration through multi-turn RL. In the first stage, a small fraction of expert trajectories is used for IL to bootstrap the agent. In the second stage, the agent iteratively predicts and executes actions, automatically collects diverse trajectories, and optimizes multiple rollouts via the GRPO objective. To further improve RL efficiency, we introduce a dynamic early-stopping strategy to prune long-tail or likely failed trajectories, along with additional engineering optimizations. Experiments show that ActiveVLN achieves the largest performance gains over IL baselines compared to both DAgger-based and prior RL-based post-training methods, while reaching competitive performance with state-of-the-art approaches despite using a smaller model. Code and data will be released soon.

Recent advances in large reasoning models have leveraged reinforcement learning with verifiable rewards (RLVR) to improve reasoning capabilities. However, scaling these methods typically requires extensive rollout computation and large datasets, leading to high training costs and low data efficiency. To mitigate this issue, we propose DEPO, a Data-Efficient Policy Optimization pipeline that combines optimized strategies for both offline and online data selection. In the offline phase, we curate a high-quality subset of training samples based on diversity, influence, and appropriate difficulty. During online RLVR training, we introduce a sample-level explorability metric to dynamically filter samples with low exploration potential, thereby reducing substantial rollout computational costs. Furthermore, we incorporate a replay mechanism for under-explored samples to ensure adequate training, which enhances the model's final convergence performance. Experiments across five reasoning benchmarks show that DEPO consistently outperforms existing methods in both offline and online data selection scenarios. Notably, using only 20% of the training data, our approach achieves a 1.85 times speed-up on AIME24 and a 1.66 times speed-up on AIME25 compared to GRPO trained on the full dataset.

Goal representation affects the performance of Hierarchical Reinforcement Learning (HRL) algorithms by decomposing the complex learning problem into easier subtasks. Recent studies show that representations that preserve temporally abstract environment dynamics are successful in solving difficult problems and provide theoretical guarantees for optimality. These methods however cannot scale to tasks where environment dynamics increase in complexity i.e. the temporally abstract transition relations depend on larger number of variables. On the other hand, other efforts have tried to use spatial abstraction to mitigate the previous issues. Their limitations include scalability to high dimensional environments and dependency on prior knowledge. In this paper, we propose a novel three-layer HRL algorithm that introduces, at different levels of the hierarchy, both a spatial and a temporal goal abstraction. We provide a theoretical study of the regret bounds of the learned policies. We evaluate the approach on complex continuous control tasks, demonstrating the effectiveness of spatial and temporal abstractions learned by this approach.

While Vision-Language Models (VLMs) post-trained with Reinforcement Learning (RL) show impressive general reasoning, their evaluation is often confined to language-dominant tasks (e.g., math). This raises a critical question: can RL post-training truly extend the inherent capability boundary of a base VLM, particularly for visual-centric spatial tasks where it initially fails? To investigate this, we introduce Ariadne, a framework utilizing synthetic mazes for multi-step spatial reasoning where task difficulty (e.g., path length, turns) is precisely controlled. We leverage this controllable environment to train VLMs using Reinforcement Learning with Verified Rewards (RLVR) in a difficulty-aware curriculum. Surprisingly, post-RLVR training, the VLM achieves over 50% accuracy on a problem set where the base model scored 0%, demonstrating that our approach expands the model's initial capability boundary. To assess real-world viability, we evaluate out-of-distribution (OOD) generalization on practical benchmarks. Despite training only on synthetic maze samples, Ariadne achieves significant zero-shot improvements, averaging 16% on MapBench (e.g., museum navigation) and 24% on ReasonMap (subway transfer tasks). These results confirm that our method not only broadens the model's fundamental limits but also enhances its generalization to real-world spatial reasoning. We acknowledge our study is limited to the post-training phase, given the opaqueness of pre-training data, and hope our research motivates further work on specialized, capability-extending alignment.

Generalization in Reinforcement Learning (RL) aims to learn an agent during training that generalizes to the target environment. This paper studies RL generalization from a theoretical aspect: how much can we expect pre-training over training environments to be helpful? When the interaction with the target environment is not allowed, we certify that the best we can obtain is a near-optimal policy in an average sense, and we design an algorithm that achieves this goal. Furthermore, when the agent is allowed to interact with the target environment, we give a surprising result showing that asymptotically, the improvement from pre-training is at most a constant factor. On the other hand, in the non-asymptotic regime, we design an efficient algorithm and prove a distribution-based regret bound in the target environment that is independent of the state-action space.

Recent high-capacity vision-language-action (VLA) models have demonstrated impressive performance on a range of robotic manipulation tasks by imitating human demonstrations. However, exploiting offline data with limited visited states will cause execution failure in out-of-distribution scenarios. Intuitively, an exploration-based method that improves on online collected data at test time could address this limitation. We present VLA-RL, an algorithmic and systematic framework that leverages online reinforcement learning (RL) to improve pretrained auto-regressive VLAs in downstream tasks. Within a unified perspective, we first introduce a trajectory-level RL formulation for auto-regressive VLA training, which models general robotic manipulation trajectory as multi-modal multi-turn conversation. To address the challenge of sparse rewards, we fine-tune a pretrained vision-language model as a robotic process reward model, which is trained on pseudo reward labels annotated on automatically extracted task segments. To scale up, we identify several implementation findings that improve the stability and efficiency including curriculum selection strategy, GPU-balanced vectorized environments, batch decoding, and critic warmup. VLA-RL enables OpenVLA-7B to surpass the strongest finetuned baseline by 4.5% on 40 challenging robotic manipulation tasks in LIBERO, and even matches the performance of advanced commercial models such as pi_0-FAST. Notably, we observe that VLA-RL benefits from increased test-time optimization, indicating an early spark of inference scaling laws in robotics.

A significant aspiration of offline reinforcement learning (RL) is to develop a generalist agent with high capabilities from large and heterogeneous datasets. However, prior approaches that scale offline RL either rely heavily on expert trajectories or struggle to generalize to diverse unseen tasks. Inspired by the excellent generalization of world model in conditional video generation, we explore the potential of image observation-based world model for scaling offline RL and enhancing generalization on novel tasks. In this paper, we introduce JOWA: Jointly-Optimized World-Action model, an offline model-based RL agent pretrained on multiple Atari games with 6 billion tokens data to learn general-purpose representation and decision-making ability. Our method jointly optimizes a world-action model through a shared transformer backbone, which stabilize temporal difference learning with large models during pretraining. Moreover, we propose a provably efficient and parallelizable planning algorithm to compensate for the Q-value estimation error and thus search out better policies. Experimental results indicate that our largest agent, with 150 million parameters, achieves 78.9% human-level performance on pretrained games using only 10% subsampled offline data, outperforming existing state-of-the-art large-scale offline RL baselines by 31.6% on averange. Furthermore, JOWA scales favorably with model capacity and can sample-efficiently transfer to novel games using only 5k offline fine-tuning data (approximately 4 trajectories) per game, demonstrating superior generalization. We will release codes and model weights at https://github.com/CJReinforce/JOWA

In machine learning for sequential decision-making, an algorithmic agent learns to interact with an environment while receiving feedback in the form of a reward signal. However, in many unstructured real-world settings, such a reward signal is unknown and humans cannot reliably craft a reward signal that correctly captures desired behavior. To solve tasks in such unstructured and open-ended environments, we present Demonstration-Inferred Preference Reinforcement Learning (DIP-RL), an algorithm that leverages human demonstrations in three distinct ways, including training an autoencoder, seeding reinforcement learning (RL) training batches with demonstration data, and inferring preferences over behaviors to learn a reward function to guide RL. We evaluate DIP-RL in a tree-chopping task in Minecraft. Results suggest that the method can guide an RL agent to learn a reward function that reflects human preferences and that DIP-RL performs competitively relative to baselines. DIP-RL is inspired by our previous work on combining demonstrations and pairwise preferences in Minecraft, which was awarded a research prize at the 2022 NeurIPS MineRL BASALT competition, Learning from Human Feedback in Minecraft. Example trajectory rollouts of DIP-RL and baselines are located at https://sites.google.com/view/dip-rl.

We introduce Reinforcement Learning (RL) with Adaptive Verifiable Environments (RLVE), an approach using verifiable environments that procedurally generate problems and provide algorithmically verifiable rewards, to scale up RL for language models (LMs). RLVE enables each verifiable environment to dynamically adapt its problem difficulty distribution to the policy model's capabilities as training progresses. In contrast, static data distributions often lead to vanishing learning signals when problems are either too easy or too hard for the policy. To implement RLVE, we create RLVE-Gym, a large-scale suite of 400 verifiable environments carefully developed through manual environment engineering. Using RLVE-Gym, we show that environment scaling, i.e., expanding the collection of training environments, consistently improves generalizable reasoning capabilities. RLVE with joint training across all 400 environments in RLVE-Gym yields a 3.37% absolute average improvement across six reasoning benchmarks, starting from one of the strongest 1.5B reasoning LMs. By comparison, continuing this LM's original RL training yields only a 0.49% average absolute gain despite using over 3x more compute. We release our code publicly.

Distribution shift is a major obstacle in offline reinforcement learning, which necessitates minimizing the discrepancy between the learned policy and the behavior policy to avoid overestimating rare or unseen actions. Previous conservative offline RL algorithms struggle to generalize to unseen actions, despite their success in learning good in-distribution policy. In contrast, we propose to use the gradient fields of the dataset density generated from a pre-trained offline RL algorithm to adjust the original actions. We decouple the conservatism constraints from the policy, thus can benefit wide offline RL algorithms. As a consequence, we propose the Conservative Denoising Score-based Algorithm (CDSA) which utilizes the denoising score-based model to model the gradient of the dataset density, rather than the dataset density itself, and facilitates a more accurate and efficient method to adjust the action generated by the pre-trained policy in a deterministic and continuous MDP environment. In experiments, we show that our approach significantly improves the performance of baseline algorithms in D4RL datasets, and demonstrate the generalizability and plug-and-play capability of our model across different pre-trained offline RL policy in different tasks. We also validate that the agent exhibits greater risk aversion after employing our method while showcasing its ability to generalize effectively across diverse tasks.

Recent advances in reinforcement learning for foundation models, such as Group Relative Policy Optimization (GRPO), have significantly improved the performance of foundation models on reasoning tasks. Notably, the advantage function serves as a central mechanism in GRPO for ranking the trajectory importance. However, existing explorations encounter both advantage reversion and advantage mirror problems, which hinder the reasonable advantage allocation across different query samples. In this work, we propose an easy but effective GRPO strategy, Mixed Advantage Policy Optimization (MAPO). We reveal that the trajectory appears with different certainty and propose the advantage percent deviation for samples with high-certainty trajectories. Furthermore, we dynamically reweight the advantage function for samples with varying trajectory certainty, thereby adaptively configuring the advantage function to account for sample-specific characteristics. Comparison with related state-of-the-art methods, along with ablation studies on different advantage variants, validates the effectiveness of our approach.

At the core of reinforcement learning is the idea of learning beyond the performance in the data. However, scaling such systems has proven notoriously tricky. In contrast, techniques from generative modeling have proven remarkably scalable and are simple to train. In this work, we combine these strengths, by deriving a direct relation between policy improvement and guidance of diffusion models. The resulting framework, CFGRL, is trained with the simplicity of supervised learning, yet can further improve on the policies in the data. On offline RL tasks, we observe a reliable trend -- increased guidance weighting leads to increased performance. Of particular importance, CFGRL can operate without explicitly learning a value function, allowing us to generalize simple supervised methods (e.g., goal-conditioned behavioral cloning) to further prioritize optimality, gaining performance for "free" across the board.

Reinforcement learning (RL) post-training is crucial for LLM alignment and reasoning, but existing policy-based methods, such as PPO and DPO, can fall short of fixing shortcuts inherited from pre-training. In this work, we introduce Qsharp, a value-based algorithm for KL-regularized RL that guides the reference policy using the optimal regularized Q function. We propose to learn the optimal Q function using distributional RL on an aggregated online dataset. Unlike prior value-based baselines that guide the model using unregularized Q-values, our method is theoretically principled and provably learns the optimal policy for the KL-regularized RL problem. Empirically, Qsharp outperforms prior baselines in math reasoning benchmarks while maintaining a smaller KL divergence to the reference policy. Theoretically, we establish a reduction from KL-regularized RL to no-regret online learning, providing the first bounds for deterministic MDPs under only realizability. Thanks to distributional RL, our bounds are also variance-dependent and converge faster when the reference policy has small variance. In sum, our results highlight Qsharp as an effective approach for post-training LLMs, offering both improved performance and theoretical guarantees. The code can be found at https://github.com/jinpz/q_sharp.

One of the key challenges of Reinforcement Learning (RL) is the ability of agents to generalise their learned policy to unseen settings. Moreover, training RL agents requires large numbers of interactions with the environment. Motivated by the recent success of Offline RL and Imitation Learning (IL), we conduct a study to investigate whether agents can leverage offline data in the form of trajectories to improve the sample-efficiency in procedurally generated environments. We consider two settings of using IL from offline data for RL: (1) pre-training a policy before online RL training and (2) concurrently training a policy with online RL and IL from offline data. We analyse the impact of the quality (optimality of trajectories) and diversity (number of trajectories and covered level) of available offline trajectories on the effectiveness of both approaches. Across four well-known sparse reward tasks in the MiniGrid environment, we find that using IL for pre-training and concurrently during online RL training both consistently improve the sample-efficiency while converging to optimal policies. Furthermore, we show that pre-training a policy from as few as two trajectories can make the difference between learning an optimal policy at the end of online training and not learning at all. Our findings motivate the widespread adoption of IL for pre-training and concurrent IL in procedurally generated environments whenever offline trajectories are available or can be generated.

Reasoning models have recently shown remarkable progress in domains such as math and coding. However, their expert-level abilities in math and coding contrast sharply with their performance in long-horizon, interactive tasks such as web navigation and computer/phone-use. Inspired by literature on human cognition, we argue that current AI agents need ''vicarious trial and error'' - the capacity to mentally simulate alternative futures before acting - in order to enhance their understanding and performance in complex interactive environments. We introduce Dyna-Mind, a two-stage training framework that explicitly teaches (V)LM agents to integrate such simulation into their reasoning. In stage 1, we introduce Reasoning with Simulations (ReSim), which trains the agent to generate structured reasoning traces from expanded search trees built from real experience gathered through environment interactions. ReSim thus grounds the agent's reasoning in faithful world dynamics and equips it with the ability to anticipate future states in its reasoning. In stage 2, we propose Dyna-GRPO, an online reinforcement learning method to further strengthen the agent's simulation and decision-making ability by using both outcome rewards and intermediate states as feedback from real rollouts. Experiments on two synthetic benchmarks (Sokoban and ALFWorld) and one realistic benchmark (AndroidWorld) demonstrate that (1) ReSim effectively infuses simulation ability into AI agents, and (2) Dyna-GRPO leverages outcome and interaction-level signals to learn better policies for long-horizon, planning-intensive tasks. Together, these results highlight the central role of simulation in enabling AI agents to reason, plan, and act more effectively in the ever more challenging environments.

In this study, we investigate the DIstribution Correction Estimation (DICE) methods, an important line of work in offline reinforcement learning (RL) and imitation learning (IL). DICE-based methods impose state-action-level behavior constraint, which is an ideal choice for offline learning. However, they typically perform much worse than current state-of-the-art (SOTA) methods that solely use action-level behavior constraint. After revisiting DICE-based methods, we find there exist two gradient terms when learning the value function using true-gradient update: forward gradient (taken on the current state) and backward gradient (taken on the next state). Using forward gradient bears a large similarity to many offline RL methods, and thus can be regarded as applying action-level constraint. However, directly adding the backward gradient may degenerate or cancel out its effect if these two gradients have conflicting directions. To resolve this issue, we propose a simple yet effective modification that projects the backward gradient onto the normal plane of the forward gradient, resulting in an orthogonal-gradient update, a new learning rule for DICE-based methods. We conduct thorough theoretical analyses and find that the projected backward gradient brings state-level behavior regularization, which reveals the mystery of DICE-based methods: the value learning objective does try to impose state-action-level constraint, but needs to be used in a corrected way. Through toy examples and extensive experiments on complex offline RL and IL tasks, we demonstrate that DICE-based methods using orthogonal-gradient updates (O-DICE) achieve SOTA performance and great robustness.

Humans often acquire new skills through observation and imitation. For robotic agents, learning from the plethora of unlabeled video demonstration data available on the Internet necessitates imitating the expert without access to its action, presenting a challenge known as Imitation Learning from Observations (ILfO). A common approach to tackle ILfO problems is to convert them into inverse reinforcement learning problems, utilizing a proxy reward computed from the agent's and the expert's observations. Nonetheless, we identify that tasks characterized by a progress dependency property pose significant challenges for such approaches; in these tasks, the agent needs to initially learn the expert's preceding behaviors before mastering the subsequent ones. Our investigation reveals that the main cause is that the reward signals assigned to later steps hinder the learning of initial behaviors. To address this challenge, we present a novel ILfO framework that enables the agent to master earlier behaviors before advancing to later ones. We introduce an Automatic Discount Scheduling (ADS) mechanism that adaptively alters the discount factor in reinforcement learning during the training phase, prioritizing earlier rewards initially and gradually engaging later rewards only when the earlier behaviors have been mastered. Our experiments, conducted on nine Meta-World tasks, demonstrate that our method significantly outperforms state-of-the-art methods across all tasks, including those that are unsolvable by them.

Dynamical generative models that produce samples through an iterative process, such as Flow Matching and denoising diffusion models, have seen widespread use, but there have not been many theoretically-sound methods for improving these models with reward fine-tuning. In this work, we cast reward fine-tuning as stochastic optimal control (SOC). Critically, we prove that a very specific memoryless noise schedule must be enforced during fine-tuning, in order to account for the dependency between the noise variable and the generated samples. We also propose a new algorithm named Adjoint Matching which outperforms existing SOC algorithms, by casting SOC problems as a regression problem. We find that our approach significantly improves over existing methods for reward fine-tuning, achieving better consistency, realism, and generalization to unseen human preference reward models, while retaining sample diversity.

We investigate the challenge of parametrizing policies for reinforcement learning (RL) in high-dimensional continuous action spaces. Our objective is to develop a multimodal policy that overcomes limitations inherent in the commonly-used Gaussian parameterization. To achieve this, we propose a principled framework that models the continuous RL policy as a generative model of optimal trajectories. By conditioning the policy on a latent variable, we derive a novel variational bound as the optimization objective, which promotes exploration of the environment. We then present a practical model-based RL method, called Reparameterized Policy Gradient (RPG), which leverages the multimodal policy parameterization and learned world model to achieve strong exploration capabilities and high data efficiency. Empirical results demonstrate that our method can help agents evade local optima in tasks with dense rewards and solve challenging sparse-reward environments by incorporating an object-centric intrinsic reward. Our method consistently outperforms previous approaches across a range of tasks. Code and supplementary materials are available on the project page https://haosulab.github.io/RPG/

Improving the performance of pre-trained policies through online reinforcement learning (RL) is a critical yet challenging topic. Existing online RL fine-tuning methods require continued training with offline pretrained Q-functions for stability and performance. However, these offline pretrained Q-functions commonly underestimate state-action pairs beyond the offline dataset due to the conservatism in most offline RL methods, which hinders further exploration when transitioning from the offline to the online setting. Additionally, this requirement limits their applicability in scenarios where only pre-trained policies are available but pre-trained Q-functions are absent, such as in imitation learning (IL) pre-training. To address these challenges, we propose a method for efficient online RL fine-tuning using solely the offline pre-trained policy, eliminating reliance on pre-trained Q-functions. We introduce PORL (Policy-Only Reinforcement Learning Fine-Tuning), which rapidly initializes the Q-function from scratch during the online phase to avoid detrimental pessimism. Our method not only achieves competitive performance with advanced offline-to-online RL algorithms and online RL approaches that leverage data or policies prior, but also pioneers a new path for directly fine-tuning behavior cloning (BC) policies.

The vast majority of Reinforcement Learning methods is largely impacted by the computation effort and data requirements needed to obtain effective estimates of action-value functions, which in turn determine the quality of the overall performance and the sample-efficiency of the learning procedure. Typically, action-value functions are estimated through an iterative scheme that alternates the application of an empirical approximation of the Bellman operator and a subsequent projection step onto a considered function space. It has been observed that this scheme can be potentially generalized to carry out multiple iterations of the Bellman operator at once, benefiting the underlying learning algorithm. However, till now, it has been challenging to effectively implement this idea, especially in high-dimensional problems. In this paper, we introduce iterated Q-Network (i-QN), a novel principled approach that enables multiple consecutive Bellman updates by learning a tailored sequence of action-value functions where each serves as the target for the next. We show that i-QN is theoretically grounded and that it can be seamlessly used in value-based and actor-critic methods. We empirically demonstrate the advantages of i-QN in Atari 2600 games and MuJoCo continuous control problems.

Reinforcement Learning with Verifiable Rewards (RLVR) has demonstrated success in enhancing LLM reasoning capabilities, but remains limited to single-turn interactions without tool integration. While recent Agentic Reinforcement Learning with Tool use (ARLT) approaches have emerged to address multi-turn tool interactions, existing works develop task-specific codebases that suffer from fragmentation, synchronous execution bottlenecks, and limited extensibility across domains. These inefficiencies hinder broader community adoption and algorithmic innovation. We introduce VerlTool, a unified and modular framework that addresses these limitations through systematic design principles. VerlTool provides four key contributions: (1) upstream alignment with VeRL ensuring compatibility and simplified maintenance, (2) unified tool management via standardized APIs supporting diverse modalities including code execution, search, SQL databases, and vision processing, (3) asynchronous rollout execution achieving near 2times speedup by eliminating synchronization bottlenecks, and (4) comprehensive evaluation demonstrating competitive performance across 6 ARLT domains. Our framework formalizes ARLT as multi-turn trajectories with multi-modal observation tokens (text/image/video), extending beyond single-turn RLVR paradigms. We train and evaluate models on mathematical reasoning, knowledge QA, SQL generation, visual reasoning, web search, and software engineering tasks, achieving results comparable to specialized systems while providing unified training infrastructure. The modular plugin architecture enables rapid tool integration requiring only lightweight Python definitions, significantly reducing development overhead and providing a scalable foundation for tool-augmented RL research. Our code is open-sourced at https://github.com/TIGER-AI-Lab/verl-tool.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a key paradigm for post-training Large Language Models (LLMs), particularly for complex reasoning tasks. However, vanilla RLVR training has been shown to improve Pass@1 performance at the expense of policy entropy, leading to reduced generation diversity and limiting the Pass@k performance, which typically represents the upper bound of LLM reasoning capability. In this paper, we systematically analyze the policy's generation diversity from the perspective of training problems and find that augmenting and updating training problems helps mitigate entropy collapse during training. Based on these observations, we propose an online Self-play with Variational problem Synthesis (SvS) strategy for RLVR training, which uses the policy's correct solutions to synthesize variational problems while ensuring their reference answers remain identical to the originals. This self-improving strategy effectively maintains policy entropy during training and substantially improves Pass@k compared with standard RLVR, sustaining prolonged improvements and achieving absolute gains of 18.3% and 22.8% in Pass@32 performance on the competition-level AIME24 and AIME25 benchmarks. Experiments on 12 reasoning benchmarks across varying model sizes from 3B to 32B consistently demonstrate the generalizability and robustness of SvS.

Adapting Large Language Models (LLMs) for agent tasks is critical in developing language agents. Direct Preference Optimization (DPO) is a promising technique for this adaptation with the alleviation of compounding errors, offering a means to directly optimize Reinforcement Learning (RL) objectives. However, applying DPO to multi-turn tasks presents challenges due to the inability to cancel the partition function. Overcoming this obstacle involves making the partition function independent of the current state and addressing length disparities between preferred and dis-preferred trajectories. In this light, we replace the policy constraint with the state-action occupancy measure constraint in the RL objective and add length normalization to the Bradley-Terry model, yielding a novel loss function named DMPO for multi-turn agent tasks with theoretical explanations. Extensive experiments on three multi-turn agent task datasets confirm the effectiveness and superiority of the DMPO loss. The code is available at https://github.com/swt-user/DMPO.

Reinforcement learning (RL) faces a persistent tension: policies that are stable to optimize are often too simple to represent the multimodal action distributions needed for complex control. Gaussian policies provide tractable likelihoods and smooth gradients, but their unimodal form limits expressiveness. Conversely, generative policies based on diffusion or flow matching can model rich multimodal behaviors; however, in online RL, they are frequently unstable due to intractable likelihoods and noisy gradients propagating through deep sampling chains. We address this tension with a key structural principle: decoupling optimization from generation. Building on this insight, we introduce GoRL (Generative Online Reinforcement Learning), a framework that optimizes a tractable latent policy while utilizing a conditional generative decoder to synthesize actions. A two-timescale update schedule enables the latent policy to learn stably while the decoder steadily increases expressiveness, without requiring tractable action likelihoods. Across a range of continuous-control tasks, GoRL consistently outperforms both Gaussian policies and recent generative-policy baselines. Notably, on the HopperStand task, it reaches a normalized return above 870, more than 3 times that of the strongest baseline. These results demonstrate that separating optimization from generation provides a practical path to policies that are both stable and highly expressive.

Recent advances in Large Language Models (LLMs) have underscored the potential of Reinforcement Learning (RL) to facilitate the emergence of reasoning capabilities. Despite the encouraging results, a fundamental dilemma persists as RL improvement relies on learning from high-quality samples, yet the exploration for such samples remains bounded by the inherent limitations of LLMs. This, in effect, creates an undesirable cycle in which what cannot be explored cannot be learned. In this work, we propose Rubric-Scaffolded Reinforcement Learning (RuscaRL), a novel instructional scaffolding framework designed to break the exploration bottleneck for general LLM reasoning. Specifically, RuscaRL introduces checklist-style rubrics as (1) explicit scaffolding for exploration during rollout generation, where different rubrics are provided as external guidance within task instructions to steer diverse high-quality responses. This guidance is gradually decayed over time, encouraging the model to internalize the underlying reasoning patterns; (2) verifiable rewards for exploitation during model training, where we can obtain robust LLM-as-a-Judge scores using rubrics as references, enabling effective RL on general reasoning tasks. Extensive experiments demonstrate the superiority of the proposed RuscaRL across various benchmarks, effectively expanding reasoning boundaries under the best-of-N evaluation. Notably, RuscaRL significantly boosts Qwen-2.5-7B-Instruct from 23.6 to 50.3 on HealthBench-500, surpassing GPT-4.1. Furthermore, our fine-tuned variant on Qwen3-30B-A3B-Instruct achieves 61.1 on HealthBench-500, outperforming leading LLMs including OpenAI-o3.

The past decade has seen vast progress in deep reinforcement learning (RL) on the back of algorithms manually designed by human researchers. Recently, it has been shown that it is possible to meta-learn update rules, with the hope of discovering algorithms that can perform well on a wide range of RL tasks. Despite impressive initial results from algorithms such as Learned Policy Gradient (LPG), there remains a generalization gap when these algorithms are applied to unseen environments. In this work, we examine how characteristics of the meta-training distribution impact the generalization performance of these algorithms. Motivated by this analysis and building on ideas from Unsupervised Environment Design (UED), we propose a novel approach for automatically generating curricula to maximize the regret of a meta-learned optimizer, in addition to a novel approximation of regret, which we name algorithmic regret (AR). The result is our method, General RL Optimizers Obtained Via Environment Design (GROOVE). In a series of experiments, we show that GROOVE achieves superior generalization to LPG, and evaluate AR against baseline metrics from UED, identifying it as a critical component of environment design in this setting. We believe this approach is a step towards the discovery of truly general RL algorithms, capable of solving a wide range of real-world environments.

With the recent rapid advancement of Agentic Intelligence, agentic tool use in LLMs has become increasingly important. During multi-turn interactions between agents and users, the dynamic, uncertain, and stochastic nature of user demands poses significant challenges to the agent's tool invocation capabilities. Agents are no longer expected to simply call tools to deliver a result; rather, they must iteratively refine their understanding of user needs through communication while simultaneously invoking tools to resolve user queries. Existing reinforcement learning (RL) approaches for tool use lack the integration of genuinely dynamic users during the RL training process. To bridge this gap, we introduce MUA-RL (Multi-turn User-interacting Agent Reinforcement Learning for agentic tool use), a novel reinforcement learning framework that, for the first time in the field of agentic tool use, integrates LLM-simulated users into the reinforcement learning loop. MUA-RL aims to enable autonomous learning of models to communicate with users efficiently and use various tools to solve practical problems in dynamic multi-turn interactions. Evaluations are done on several multi-turn tool-using benchmarks (see Figure 1). Specifically, MUA-RL-32B achieves 67.3 on TAU2 Retail, 45.4 on TAU2 Airline, 28.3 on TAU2 Telecom, 28.4 on BFCL-V3 Multi Turn, and 82.5 on ACEBench Agent -- outperforming or matching the performance of larger open-source models such as DeepSeek-V3-0324 and Qwen3-235B-A22B in non-thinking settings.

Model-agnostic meta-reinforcement learning requires estimating the Hessian matrix of value functions. This is challenging from an implementation perspective, as repeatedly differentiating policy gradient estimates may lead to biased Hessian estimates. In this work, we provide a unifying framework for estimating higher-order derivatives of value functions, based on off-policy evaluation. Our framework interprets a number of prior approaches as special cases and elucidates the bias and variance trade-off of Hessian estimates. This framework also opens the door to a new family of estimates, which can be easily implemented with auto-differentiation libraries, and lead to performance gains in practice.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a promising framework for improving reasoning abilities in Large Language Models (LLMs). However, policy optimized with binary verification prone to overlook potential valuable exploration in reasoning trajectory. In view of heavy annotation cost of golden Process Reward Models (PRMs), recent works attempt using auxiliary signals for reward shaping of process tokens, involving entropy and likelihood collected from logit space. In this work, we offer a novel perspective on shaping RLVR with flow rewards derived from latent space, and propose RLFR, where the flow fields of model latents are constructed from either off-policy high-quality data and on-policy rejection sampling data, and the velocity deviations of policy latents within it are quantified to serve as a reward signal. RLFR first demonstrates that a well-established flow field can be a sound environment for reward signal collection, highlighting the expressive latent space is much underexplored. Moreover, RLFR is able to compress any off-policy expert data as reference for constituting reward signals, and we show that the efficient context dependence compressed within the hidden states are utilized, rather than individual token-level denotation for context comprehending. Experiments on both language and multimodal reasoning benchmarks demonstrate the reliability of flow rewards, and suggesting a promising paradigm for reward shaping with auxiliary signals.

Recent improvements in conditional generative modeling have made it possible to generate high-quality images from language descriptions alone. We investigate whether these methods can directly address the problem of sequential decision-making. We view decision-making not through the lens of reinforcement learning (RL), but rather through conditional generative modeling. To our surprise, we find that our formulation leads to policies that can outperform existing offline RL approaches across standard benchmarks. By modeling a policy as a return-conditional diffusion model, we illustrate how we may circumvent the need for dynamic programming and subsequently eliminate many of the complexities that come with traditional offline RL. We further demonstrate the advantages of modeling policies as conditional diffusion models by considering two other conditioning variables: constraints and skills. Conditioning on a single constraint or skill during training leads to behaviors at test-time that can satisfy several constraints together or demonstrate a composition of skills. Our results illustrate that conditional generative modeling is a powerful tool for decision-making.

Recent Reinforcement Learning (RL) algorithms making use of Kullback-Leibler (KL) regularization as a core component have shown outstanding performance. Yet, only little is understood theoretically about why KL regularization helps, so far. We study KL regularization within an approximate value iteration scheme and show that it implicitly averages q-values. Leveraging this insight, we provide a very strong performance bound, the very first to combine two desirable aspects: a linear dependency to the horizon (instead of quadratic) and an error propagation term involving an averaging effect of the estimation errors (instead of an accumulation effect). We also study the more general case of an additional entropy regularizer. The resulting abstract scheme encompasses many existing RL algorithms. Some of our assumptions do not hold with neural networks, so we complement this theoretical analysis with an extensive empirical study.

Value function factorization has achieved great success in multi-agent reinforcement learning by optimizing joint action-value functions through the maximization of factorized per-agent utilities. To ensure Individual-Global-Maximum property, existing works often focus on value factorization using monotonic functions, which are known to result in restricted representation expressiveness. In this paper, we analyze the limitations of monotonic factorization and present ConcaveQ, a novel non-monotonic value function factorization approach that goes beyond monotonic mixing functions and employs neural network representations of concave mixing functions. Leveraging the concave property in factorization, an iterative action selection scheme is developed to obtain optimal joint actions during training. It is used to update agents' local policy networks, enabling fully decentralized execution. The effectiveness of the proposed ConcaveQ is validated across scenarios involving multi-agent predator-prey environment and StarCraft II micromanagement tasks. Empirical results exhibit significant improvement of ConcaveQ over state-of-the-art multi-agent reinforcement learning approaches.

Deep Reinforcement Learning (DRL) in simulation often results in brittle and unrealistic learning outcomes. To push the agent towards more desirable solutions, prior information can be injected in the learning process through, for instance, reward shaping, expert data, or motion primitives. We propose an additional inductive bias for robot learning: latent actions learned from expert demonstration as priors in the action space. We show that these action priors can be learned from only a single open-loop gait cycle using a simple autoencoder. Using these latent action priors combined with established style rewards for imitation in DRL achieves above expert demonstration level of performance and leads to more desirable gaits. Further, action priors substantially improve the performance on transfer tasks, even leading to gait transitions for higher target speeds. Videos and code are available at https://sites.google.com/view/latent-action-priors.