Daily Papers

Integral reinforcement learning (IntRL) demands the precise computation of the utility function's integral at its policy evaluation (PEV) stage. This is achieved through quadrature rules, which are weighted sums of utility functions evaluated from state samples obtained in discrete time. Our research reveals a critical yet underexplored phenomenon: the choice of the computational method -- in this case, the quadrature rule -- can significantly impact control performance. This impact is traced back to the fact that computational errors introduced in the PEV stage can affect the policy iteration's convergence behavior, which in turn affects the learned controller. To elucidate how computation impacts control, we draw a parallel between IntRL's policy iteration and Newton's method applied to the Hamilton-Jacobi-Bellman equation. In this light, computational error in PEV manifests as an extra error term in each iteration of Newton's method, with its upper bound proportional to the computational error. Further, we demonstrate that when the utility function resides in a reproducing kernel Hilbert space (RKHS), the optimal quadrature is achievable by employing Bayesian quadrature with the RKHS-inducing kernel function. We prove that the local convergence rates for IntRL using the trapezoidal rule and Bayesian quadrature with a Mat\'ern kernel to be O(N^{-2}) and O(N^{-b}), where N is the number of evenly-spaced samples and b is the Mat\'ern kernel's smoothness parameter. These theoretical findings are finally validated by two canonical control tasks.

While reinforcement learning (RL) has shown promising performance, its sample complexity continues to be a substantial hurdle, restricting its broader application across a variety of domains. Imitation learning (IL) utilizes oracles to improve sample efficiency, yet it is often constrained by the quality of the oracles deployed. which actively interleaves between IL and RL based on an online estimate of their performance. RPI draws on the strengths of IL, using oracle queries to facilitate exploration, an aspect that is notably challenging in sparse-reward RL, particularly during the early stages of learning. As learning unfolds, RPI gradually transitions to RL, effectively treating the learned policy as an improved oracle. This algorithm is capable of learning from and improving upon a diverse set of black-box oracles. Integral to RPI are Robust Active Policy Selection (RAPS) and Robust Policy Gradient (RPG), both of which reason over whether to perform state-wise imitation from the oracles or learn from its own value function when the learner's performance surpasses that of the oracles in a specific state. Empirical evaluations and theoretical analysis validate that RPI excels in comparison to existing state-of-the-art methodologies, demonstrating superior performance across various benchmark domains.

Large Language Models (LLMs) have shown remarkable capabilities in reasoning, exemplified by the success of OpenAI-o1 and DeepSeek-R1. However, integrating reasoning with external search processes remains challenging, especially for complex multi-hop questions requiring multiple retrieval steps. We propose ReSearch, a novel framework that trains LLMs to Reason with Search via reinforcement learning without using any supervised data on reasoning steps. Our approach treats search operations as integral components of the reasoning chain, where when and how to perform searches is guided by text-based thinking, and search results subsequently influence further reasoning. We train ReSearch on Qwen2.5-7B(-Instruct) and Qwen2.5-32B(-Instruct) models and conduct extensive experiments. Despite being trained on only one dataset, our models demonstrate strong generalizability across various benchmarks. Analysis reveals that ReSearch naturally elicits advanced reasoning capabilities such as reflection and self-correction during the reinforcement learning process.

Evaluations of Deep Reinforcement Learning (DRL) methods are an integral part of scientific progress of the field. Beyond designing DRL methods for general intelligence, designing task-specific methods is becoming increasingly prominent for real-world applications. In these settings, the standard evaluation practice involves using a few instances of Markov Decision Processes (MDPs) to represent the task. However, many tasks induce a large family of MDPs owing to variations in the underlying environment, particularly in real-world contexts. For example, in traffic signal control, variations may stem from intersection geometries and traffic flow levels. The select MDP instances may thus inadvertently cause overfitting, lacking the statistical power to draw conclusions about the method's true performance across the family. In this article, we augment DRL evaluations to consider parameterized families of MDPs. We show that in comparison to evaluating DRL methods on select MDP instances, evaluating the MDP family often yields a substantially different relative ranking of methods, casting doubt on what methods should be considered state-of-the-art. We validate this phenomenon in standard control benchmarks and the real-world application of traffic signal control. At the same time, we show that accurately evaluating on an MDP family is nontrivial. Overall, this work identifies new challenges for empirical rigor in reinforcement learning, especially as the outcomes of DRL trickle into downstream decision-making.

In this paper, we propose Bootstrapped Language-Image Pretraining-driven Fused State Representation in Proximal Policy Optimization (BLIP-FusePPO), a novel multimodal reinforcement learning (RL) framework for autonomous lane-keeping (LK), in which semantic embeddings generated by a vision-language model (VLM) are directly fused with geometric states, LiDAR observations, and Proportional-Integral-Derivative-based (PID) control feedback within the agent observation space. The proposed method lets the agent learn driving rules that are aware of their surroundings and easy to understand by combining high-level scene understanding from the VLM with low-level control and spatial signals. Our architecture brings together semantic, geometric, and control-aware representations to make policy learning more robust. A hybrid reward function that includes semantic alignment, LK accuracy, obstacle avoidance, and speed regulation helps learning to be more efficient and generalizable. Our method is different from the approaches that only use semantic models to shape rewards. Instead, it directly embeds semantic features into the state representation. This cuts down on expensive runtime inference and makes sure that semantic guidance is always available. The simulation results show that the proposed model is better at LK stability and adaptability than the best vision-based and multimodal RL baselines in a wide range of difficult driving situations. We make our code publicly available.

Diffusion models have achieved impressive results in generative tasks like text-to-image (T2I) and text-to-video (T2V) synthesis. However, achieving accurate text alignment in T2V generation remains challenging due to the complex temporal dependency across frames. Existing reinforcement learning (RL)-based approaches to enhance text alignment often require differentiable reward functions or are constrained to limited prompts, hindering their scalability and applicability. In this paper, we propose Free^2Guide, a novel gradient-free framework for aligning generated videos with text prompts without requiring additional model training. Leveraging principles from path integral control, Free^2Guide approximates guidance for diffusion models using non-differentiable reward functions, thereby enabling the integration of powerful black-box Large Vision-Language Models (LVLMs) as reward model. Additionally, our framework supports the flexible ensembling of multiple reward models, including large-scale image-based models, to synergistically enhance alignment without incurring substantial computational overhead. We demonstrate that Free^2Guide significantly improves text alignment across various dimensions and enhances the overall quality of generated videos.

Long-term training of large language models (LLMs) requires maintaining stable exploration to prevent the model from collapsing into sub-optimal behaviors. Entropy is crucial in this context, as it controls exploration and helps avoid premature convergence to sub-optimal solutions. However, existing reinforcement learning methods struggle to maintain an appropriate level of entropy, as the training process involves a mix of positive and negative samples, each affecting entropy in different ways across steps. To address this, we propose Entropy stablilization via Proportional-Integral Control (EntroPIC), a novel method that adaptively adjusts the influence of positive and negative samples by dynamically tuning their loss coefficients. This approach stabilizes entropy throughout training, ensuring efficient exploration and steady progress. We provide a comprehensive theoretical analysis for both on-policy and off-policy learning settings, demonstrating that EntroPIC is effective at controlling entropy in large-scale LLM training. Experimental results show that our method successfully maintains desired entropy levels, enabling stable and optimal RL training for LLMs.

Integral to recent successes in deep reinforcement learning has been a class of temporal difference methods that use infrequently updated target values for policy evaluation in a Markov Decision Process. Yet a complete theoretical explanation for the effectiveness of target networks remains elusive. In this work, we provide an analysis of this popular class of algorithms, to finally answer the question: `why do target networks stabilise TD learning'? To do so, we formalise the notion of a partially fitted policy evaluation method, which describes the use of target networks and bridges the gap between fitted methods and semigradient temporal difference algorithms. Using this framework we are able to uniquely characterise the so-called deadly triad - the use of TD updates with (nonlinear) function approximation and off-policy data - which often leads to nonconvergent algorithms. This insight leads us to conclude that the use of target networks can mitigate the effects of poor conditioning in the Jacobian of the TD update. Instead, we show that under mild regularity conditions and a well tuned target network update frequency, convergence can be guaranteed even in the extremely challenging off-policy sampling and nonlinear function approximation setting.

In this study, we propose Shortcut Fine-Tuning (SFT), a new approach for addressing the challenge of fast sampling of pretrained Denoising Diffusion Probabilistic Models (DDPMs). SFT advocates for the fine-tuning of DDPM samplers through the direct minimization of Integral Probability Metrics (IPM), instead of learning the backward diffusion process. This enables samplers to discover an alternative and more efficient sampling shortcut, deviating from the backward diffusion process. Inspired by a control perspective, we propose a new algorithm SFT-PG: Shortcut Fine-Tuning with Policy Gradient, and prove that under certain assumptions, gradient descent of diffusion models with respect to IPM is equivalent to performing policy gradient. To our best knowledge, this is the first attempt to utilize reinforcement learning (RL) methods to train diffusion models. Through empirical evaluation, we demonstrate that our fine-tuning method can further enhance existing fast DDPM samplers, resulting in sample quality comparable to or even surpassing that of the full-step model across various datasets.

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.

Training large language models (LLMs) for complex reasoning via Reinforcement Learning with Verifiable Rewards (RLVR) is effective but limited by reliance on costly, domain-specific supervision. We explore Reinforcement Learning from Internal Feedback (RLIF), a framework that enables LLMs to learn from intrinsic signals without external rewards or labeled data. We propose Intuitor, an RLIF method that uses a model's own confidence, termed self-certainty, as its sole reward signal. Intuitor replaces external rewards in Group Relative Policy Optimization (GRPO) with self-certainty scores, enabling fully unsupervised learning. Experiments demonstrate that Intuitor matches GRPO's performance on mathematical benchmarks while achieving superior generalization to out-of-domain tasks like code generation, without requiring gold solutions or test cases. Our findings show that intrinsic model signals can drive effective learning across domains, offering a scalable alternative to RLVR for autonomous AI systems where verifiable rewards are unavailable. Code is available at https://github.com/sunblaze-ucb/Intuitor

Reinforcement learning (RL) allows an agent interacting sequentially with an environment to maximize its long-term expected return. In the distributional RL (DistrRL) paradigm, the agent goes beyond the limit of the expected value, to capture the underlying probability distribution of the return across all time steps. The set of DistrRL algorithms has led to improved empirical performance. Nevertheless, the theory of DistrRL is still not fully understood, especially in the control case. In this paper, we present the simpler one-step distributional reinforcement learning (OS-DistrRL) framework encompassing only the randomness induced by the one-step dynamics of the environment. Contrary to DistrRL, we show that our approach comes with a unified theory for both policy evaluation and control. Indeed, we propose two OS-DistrRL algorithms for which we provide an almost sure convergence analysis. The proposed approach compares favorably with categorical DistrRL on various environments.

We present a general convergent class of reinforcement learning algorithms that is founded on two distinct principles: (1) mapping value estimates to a different space using arbitrary functions from a broad class, and (2) linearly decomposing the reward signal into multiple channels. The first principle enables incorporating specific properties into the value estimator that can enhance learning. The second principle, on the other hand, allows for the value function to be represented as a composition of multiple utility functions. This can be leveraged for various purposes, e.g. dealing with highly varying reward scales, incorporating a priori knowledge about the sources of reward, and ensemble learning. Combining the two principles yields a general blueprint for instantiating convergent algorithms by orchestrating diverse mapping functions over multiple reward channels. This blueprint generalizes and subsumes algorithms such as Q-Learning, Log Q-Learning, and Q-Decomposition. In addition, our convergence proof for this general class relaxes certain required assumptions in some of these algorithms. Based on our theory, we discuss several interesting configurations as special cases. Finally, to illustrate the potential of the design space that our theory opens up, we instantiate a particular algorithm and evaluate its performance on the Atari suite.

Two common approaches to sequential decision-making are AI planning (AIP) and reinforcement learning (RL). Each has strengths and weaknesses. AIP is interpretable, easy to integrate with symbolic knowledge, and often efficient, but requires an up-front logical domain specification and is sensitive to noise; RL only requires specification of rewards and is robust to noise but is sample inefficient and not easily supplied with external knowledge. We propose an integrative approach that combines high-level planning with RL, retaining interpretability, transfer, and efficiency, while allowing for robust learning of the lower-level plan actions. Our approach defines options in hierarchical reinforcement learning (HRL) from AIP operators by establishing a correspondence between the state transition model of AI planning problem and the abstract state transition system of a Markov Decision Process (MDP). Options are learned by adding intrinsic rewards to encourage consistency between the MDP and AIP transition models. We demonstrate the benefit of our integrated approach by comparing the performance of RL and HRL algorithms in both MiniGrid and N-rooms environments, showing the advantage of our method over the existing ones.

Electric motors are used in many applications and their efficiency is strongly dependent on their control. Among others, PI approaches or model predictive control methods are well-known in the scientific literature and industrial practice. A novel approach is to use reinforcement learning (RL) to have an agent learn electric drive control from scratch merely by interacting with a suitable control environment. RL achieved remarkable results with super-human performance in many games (e.g. Atari classics or Go) and also becomes more popular in control tasks like cartpole or swinging pendulum benchmarks. In this work, the open-source Python package gym-electric-motor (GEM) is developed for ease of training of RL-agents for electric motor control. Furthermore, this package can be used to compare the trained agents with other state-of-the-art control approaches. It is based on the OpenAI Gym framework that provides a widely used interface for the evaluation of RL-agents. The initial package version covers different DC motor variants and the prevalent permanent magnet synchronous motor as well as different power electronic converters and a mechanical load model. Due to the modular setup of the proposed toolbox, additional motor, load, and power electronic devices can be easily extended in the future. Furthermore, different secondary effects like controller interlocking time or noise are considered. An intelligent controller example based on the deep deterministic policy gradient algorithm which controls a series DC motor is presented and compared to a cascaded PI-controller as a baseline for future research. Fellow researchers are encouraged to use the framework in their RL investigations or to contribute to the functional scope (e.g. further motor types) of the package.

This work presents In-Context Policy Iteration, an algorithm for performing Reinforcement Learning (RL), in-context, using foundation models. While the application of foundation models to RL has received considerable attention, most approaches rely on either (1) the curation of expert demonstrations (either through manual design or task-specific pretraining) or (2) adaptation to the task of interest using gradient methods (either fine-tuning or training of adapter layers). Both of these techniques have drawbacks. Collecting demonstrations is labor-intensive, and algorithms that rely on them do not outperform the experts from which the demonstrations were derived. All gradient techniques are inherently slow, sacrificing the "few-shot" quality that made in-context learning attractive to begin with. In this work, we present an algorithm, ICPI, that learns to perform RL tasks without expert demonstrations or gradients. Instead we present a policy-iteration method in which the prompt content is the entire locus of learning. ICPI iteratively updates the contents of the prompt from which it derives its policy through trial-and-error interaction with an RL environment. In order to eliminate the role of in-weights learning (on which approaches like Decision Transformer rely heavily), we demonstrate our algorithm using Codex, a language model with no prior knowledge of the domains on which we evaluate it.

This work presents a novel algorithm that integrates a data-efficient function approximator with reinforcement learning in continuous state spaces. An online and incremental algorithm capable of learning from a single pass through data, called Incremental Gaussian Mixture Network (IGMN), was employed as a sample-efficient function approximator for the joint state and Q-values space, all in a single model, resulting in a concise and data-efficient algorithm, i.e., a reinforcement learning algorithm that learns from very few interactions with the environment. Results are analyzed to explain the properties of the obtained algorithm, and it is observed that the use of the IGMN function approximator brings some important advantages to reinforcement learning in relation to conventional neural networks trained by gradient descent methods.

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.

As systems trend toward superintelligence, a natural modeling premise is that agents can self-improve along every facet of their own design. We formalize this with a five-axis decomposition and a decision layer, separating incentives from learning behavior and analyzing axes in isolation. Our central result identifies and introduces a sharp utility--learning tension, the structural conflict in self-modifying systems whereby utility-driven changes that improve immediate or expected performance can also erode the statistical preconditions for reliable learning and generalization. Our findings show that distribution-free guarantees are preserved iff the policy-reachable model family is uniformly capacity-bounded; when capacity can grow without limit, utility-rational self-changes can render learnable tasks unlearnable. Under standard assumptions common in practice, these axes reduce to the same capacity criterion, yielding a single boundary for safe self-modification. Numerical experiments across several axes validate the theory by comparing destructive utility policies against our proposed two-gate policies that preserve learnability.

Training reinforcement learning (RL) agents on robotic tasks typically requires a large number of training samples. This is because training data often consists of noisy trajectories, whether from exploration or human-collected demonstrations, making it difficult to learn value functions that understand the effect of taking each action. On the other hand, recent behavior-cloning (BC) approaches have shown that predicting a sequence of actions enables policies to effectively approximate noisy, multi-modal distributions of expert demonstrations. Can we use a similar idea for improving RL on robotic tasks? In this paper, we introduce a novel RL algorithm that learns a critic network that outputs Q-values over a sequence of actions. By explicitly training the value functions to learn the consequence of executing a series of current and future actions, our algorithm allows for learning useful value functions from noisy trajectories. We study our algorithm across various setups with sparse and dense rewards, and with or without demonstrations, spanning mobile bi-manual manipulation, whole-body control, and tabletop manipulation tasks from BiGym, HumanoidBench, and RLBench. We find that, by learning the critic network with action sequences, our algorithm outperforms various RL and BC baselines, in particular on challenging humanoid control tasks.

We study a class of reinforcement learning problems where the reward signals for policy learning are generated by a discriminator that is dependent on and jointly optimized with the policy. This interdependence between the policy and the discriminator leads to an unstable learning process because reward signals from an immature discriminator are noisy and impede policy learning, and conversely, an untrained policy impedes discriminator learning. We call this learning setting Internally Rewarded Reinforcement Learning (IRRL) as the reward is not provided directly by the environment but internally by the discriminator. In this paper, we formally formulate IRRL and present a class of problems that belong to IRRL. We theoretically derive and empirically analyze the effect of the reward function in IRRL and based on these analyses propose the clipped linear reward function. Experimental results show that the proposed reward function can consistently stabilize the training process by reducing the impact of reward noise, which leads to faster convergence and higher performance compared with baselines in diverse tasks.

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.

We consider the reinforcement learning (RL) problem with general utilities which consists in maximizing a function of the state-action occupancy measure. Beyond the standard cumulative reward RL setting, this problem includes as particular cases constrained RL, pure exploration and learning from demonstrations among others. For this problem, we propose a simpler single-loop parameter-free normalized policy gradient algorithm. Implementing a recursive momentum variance reduction mechanism, our algorithm achieves mathcal{O}(epsilon^{-3}) and mathcal{O}(epsilon^{-2}) sample complexities for epsilon-first-order stationarity and epsilon-global optimality respectively, under adequate assumptions. We further address the setting of large finite state action spaces via linear function approximation of the occupancy measure and show a mathcal{O}(epsilon^{-4}) sample complexity for a simple policy gradient method with a linear regression subroutine.

It is well known that ensemble methods often provide enhanced performance in reinforcement learning. In this paper, we explore this concept further by using group-aided training within the distributional reinforcement learning paradigm. Specifically, we propose an extension to categorical reinforcement learning, where distributional learning targets are implicitly based on the total information gathered by an ensemble. We empirically show that this may lead to much more robust initial learning, a stronger individual performance level, and good efficiency on a per-sample basis.

Extrinsic rewards can effectively guide reinforcement learning (RL) agents in specific tasks. However, extrinsic rewards frequently fall short in complex environments due to the significant human effort needed for their design and annotation. This limitation underscores the necessity for intrinsic rewards, which offer auxiliary and dense signals and can enable agents to learn in an unsupervised manner. Although various intrinsic reward formulations have been proposed, their implementation and optimization details are insufficiently explored and lack standardization, thereby hindering research progress. To address this gap, we introduce RLeXplore, a unified, highly modularized, and plug-and-play framework offering reliable implementations of eight state-of-the-art intrinsic reward methods. Furthermore, we conduct an in-depth study that identifies critical implementation details and establishes well-justified standard practices in intrinsically-motivated RL. Our documentation, examples, and source code are available at https://github.com/RLE-Foundation/RLeXplore.

Data-driven methods such as reinforcement and imitation learning have achieved remarkable success in robot autonomy. However, their data-centric nature still hinders them from generalizing well to ever-changing environments. Moreover, collecting large datasets for robotic tasks is often impractical and expensive. To overcome these challenges, we introduce a new self-supervised neural-symbolic (NeSy) computational framework, imperative learning (IL), for robot autonomy, leveraging the generalization abilities of symbolic reasoning. The framework of IL consists of three primary components: a neural module, a reasoning engine, and a memory system. We formulate IL as a special bilevel optimization (BLO), which enables reciprocal learning over the three modules. This overcomes the label-intensive obstacles associated with data-driven approaches and takes advantage of symbolic reasoning concerning logical reasoning, physical principles, geometric analysis, etc. We discuss several optimization techniques for IL and verify their effectiveness in five distinct robot autonomy tasks including path planning, rule induction, optimal control, visual odometry, and multi-robot routing. Through various experiments, we show that IL can significantly enhance robot autonomy capabilities and we anticipate that it will catalyze further research across diverse domains.

Most deep reinforcement learning (RL) algorithms distill experience into parametric behavior policies or value functions via gradient updates. While effective, this approach has several disadvantages: (1) it is computationally expensive, (2) it can take many updates to integrate experiences into the parametric model, (3) experiences that are not fully integrated do not appropriately influence the agent's behavior, and (4) behavior is limited by the capacity of the model. In this paper we explore an alternative paradigm in which we train a network to map a dataset of past experiences to optimal behavior. Specifically, we augment an RL agent with a retrieval process (parameterized as a neural network) that has direct access to a dataset of experiences. This dataset can come from the agent's past experiences, expert demonstrations, or any other relevant source. The retrieval process is trained to retrieve information from the dataset that may be useful in the current context, to help the agent achieve its goal faster and more efficiently. he proposed method facilitates learning agents that at test-time can condition their behavior on the entire dataset and not only the current state, or current trajectory. We integrate our method into two different RL agents: an offline DQN agent and an online R2D2 agent. In offline multi-task problems, we show that the retrieval-augmented DQN agent avoids task interference and learns faster than the baseline DQN agent. On Atari, we show that retrieval-augmented R2D2 learns significantly faster than the baseline R2D2 agent and achieves higher scores. We run extensive ablations to measure the contributions of the components of our proposed method.

We consider the problem of preference based reinforcement learning (PbRL), where, unlike traditional reinforcement learning, an agent receives feedback only in terms of a 1 bit (0/1) preference over a trajectory pair instead of absolute rewards for them. The success of the traditional RL framework crucially relies on the underlying agent-reward model, which, however, depends on how accurately a system designer can express an appropriate reward function and often a non-trivial task. The main novelty of our framework is the ability to learn from preference-based trajectory feedback that eliminates the need to hand-craft numeric reward models. This paper sets up a formal framework for the PbRL problem with non-markovian rewards, where the trajectory preferences are encoded by a generalized linear model of dimension d. Assuming the transition model is known, we then propose an algorithm with almost optimal regret guarantee of mathcal{O}left( SH d log (T / delta) T right). We further, extend the above algorithm to the case of unknown transition dynamics, and provide an algorithm with near optimal regret guarantee mathcal{O}((d + H^2 + |S|)dT +|mathcal{S||A|TH} ). To the best of our knowledge, our work is one of the first to give tight regret guarantees for preference based RL problems with trajectory preferences.

We study reward-free reinforcement learning (RL) with linear function approximation, where the agent works in two phases: (1) in the exploration phase, the agent interacts with the environment but cannot access the reward; and (2) in the planning phase, the agent is given a reward function and is expected to find a near-optimal policy based on samples collected in the exploration phase. The sample complexities of existing reward-free algorithms have a polynomial dependence on the planning horizon, which makes them intractable for long planning horizon RL problems. In this paper, we propose a new reward-free algorithm for learning linear mixture Markov decision processes (MDPs), where the transition probability can be parameterized as a linear combination of known feature mappings. At the core of our algorithm is uncertainty-weighted value-targeted regression with exploration-driven pseudo-reward and a high-order moment estimator for the aleatoric and epistemic uncertainties. When the total reward is bounded by 1, we show that our algorithm only needs to explore tilde O( d^2varepsilon^{-2}) episodes to find an varepsilon-optimal policy, where d is the dimension of the feature mapping. The sample complexity of our algorithm only has a polylogarithmic dependence on the planning horizon and therefore is ``horizon-free''. In addition, we provide an Omega(d^2varepsilon^{-2}) sample complexity lower bound, which matches the sample complexity of our algorithm up to logarithmic factors, suggesting that our algorithm is optimal.

Offline reinforcement learning (RL) aims to learn an optimal policy from pre-collected data. However, it faces challenges of distributional shift, where the learned policy may encounter unseen scenarios not covered in the offline data. Additionally, numerous applications suffer from a scarcity of labeled reward data. Relying on labeled data alone often leads to a narrow state-action distribution, further amplifying the distributional shift, and resulting in suboptimal policy learning. To address these issues, we first recognize that the volume of unlabeled data is typically substantially larger than that of labeled data. We then propose a semi-pessimistic RL method to effectively leverage abundant unlabeled data. Our approach offers several advantages. It considerably simplifies the learning process, as it seeks a lower bound of the reward function, rather than that of the Q-function or state transition function. It is highly flexible, and can be integrated with a range of model-free and model-based RL algorithms. It enjoys the guaranteed improvement when utilizing vast unlabeled data, but requires much less restrictive conditions. We compare our method with a number of alternative solutions, both analytically and numerically, and demonstrate its clear competitiveness. We further illustrate with an application to adaptive deep brain stimulation for Parkinson's disease.

Reinforcement learning (RL) problems can be challenging without well-shaped rewards. Prior work on provably efficient RL methods generally proposes to address this issue with dedicated exploration strategies. However, another way to tackle this challenge is to reformulate it as a multi-task RL problem, where the task space contains not only the challenging task of interest but also easier tasks that implicitly function as a curriculum. Such a reformulation opens up the possibility of running existing multi-task RL methods as a more efficient alternative to solving a single challenging task from scratch. In this work, we provide a theoretical framework that reformulates a single-task RL problem as a multi-task RL problem defined by a curriculum. Under mild regularity conditions on the curriculum, we show that sequentially solving each task in the multi-task RL problem is more computationally efficient than solving the original single-task problem, without any explicit exploration bonuses or other exploration strategies. We also show that our theoretical insights can be translated into an effective practical learning algorithm that can accelerate curriculum learning on simulated robotic tasks.

Reinforcement learning (RL) algorithms aim to balance exploiting the current best strategy with exploring new options that could lead to higher rewards. Most common RL algorithms use undirected exploration, i.e., select random sequences of actions. Exploration can also be directed using intrinsic rewards, such as curiosity or model epistemic uncertainty. However, effectively balancing task and intrinsic rewards is challenging and often task-dependent. In this work, we introduce a framework, MaxInfoRL, for balancing intrinsic and extrinsic exploration. MaxInfoRL steers exploration towards informative transitions, by maximizing intrinsic rewards such as the information gain about the underlying task. When combined with Boltzmann exploration, this approach naturally trades off maximization of the value function with that of the entropy over states, rewards, and actions. We show that our approach achieves sublinear regret in the simplified setting of multi-armed bandits. We then apply this general formulation to a variety of off-policy model-free RL methods for continuous state-action spaces, yielding novel algorithms that achieve superior performance across hard exploration problems and complex scenarios such as visual control tasks.

Reinforcement learning (RL) has enabled machine learning models to achieve significant advances in many fields. Most recently, RL has empowered frontier language models to solve challenging math, science, and coding problems. However, central to any RL algorithm is the reward function, and reward engineering is a notoriously difficult problem in any domain. In this paper, we propose RENT: Reinforcement Learning via Entropy Minimization -- a fully unsupervised RL method that requires no external reward or ground-truth answers, and instead uses the model's entropy of its underlying distribution as an intrinsic reward. We find that by reinforcing the chains of thought that yield high model confidence on its generated answers, the model improves its reasoning ability. In our experiments, we showcase these improvements on an extensive suite of commonly-used reasoning benchmarks, including GSM8K, MATH500, AMC, AIME, and GPQA, and models of varying sizes from the Qwen, Mistral, and Llama families. The generality of our unsupervised learning method lends itself to applicability in a wide range of domains where external supervision is unavailable.

Although reinforcement learning methods offer a powerful framework for automatic skill acquisition, for practical learning-based control problems in domains such as robotics, imitation learning often provides a more convenient and accessible alternative. In particular, an interactive imitation learning method such as DAgger, which queries a near-optimal expert to intervene online to collect correction data for addressing the distributional shift challenges that afflict na\"ive behavioral cloning, can enjoy good performance both in theory and practice without requiring manually specified reward functions and other components of full reinforcement learning methods. In this paper, we explore how off-policy reinforcement learning can enable improved performance under assumptions that are similar but potentially even more practical than those of interactive imitation learning. Our proposed method uses reinforcement learning with user intervention signals themselves as rewards. This relaxes the assumption that intervening experts in interactive imitation learning should be near-optimal and enables the algorithm to learn behaviors that improve over the potential suboptimal human expert. We also provide a unified framework to analyze our RL method and DAgger; for which we present the asymptotic analysis of the suboptimal gap for both methods as well as the non-asymptotic sample complexity bound of our method. We then evaluate our method on challenging high-dimensional continuous control simulation benchmarks as well as real-world robotic vision-based manipulation tasks. The results show that it strongly outperforms DAgger-like approaches across the different tasks, especially when the intervening experts are suboptimal. Code and videos can be found on the project website: rlif-page.github.io

Reward functions are difficult to design and often hard to align with human intent. Preference-based Reinforcement Learning (RL) algorithms address these problems by learning reward functions from human feedback. However, the majority of preference-based RL methods na\"ively combine supervised reward models with off-the-shelf RL algorithms. Contemporary approaches have sought to improve performance and query complexity by using larger and more complex reward architectures such as transformers. Instead of using highly complex architectures, we develop a new and parameter-efficient algorithm, Inverse Preference Learning (IPL), specifically designed for learning from offline preference data. Our key insight is that for a fixed policy, the Q-function encodes all information about the reward function, effectively making them interchangeable. Using this insight, we completely eliminate the need for a learned reward function. Our resulting algorithm is simpler and more parameter-efficient. Across a suite of continuous control and robotics benchmarks, IPL attains competitive performance compared to more complex approaches that leverage transformer-based and non-Markovian reward functions while having fewer algorithmic hyperparameters and learned network parameters. Our code is publicly released.

In this paper, a unified framework for exploration in reinforcement learning (RL) is proposed based on an option-critic model. The proposed framework learns to integrate a set of diverse exploration strategies so that the agent can adaptively select the most effective exploration strategy over time to realize a relevant exploration-exploitation trade-off for each given task. The effectiveness of the proposed exploration framework is demonstrated by various experiments in the MiniGrid and Atari environments.

A growing trend for value-based reinforcement learning (RL) algorithms is to capture more information than scalar value functions in the value network. One of the most well-known methods in this branch is distributional RL, which models return distribution instead of scalar value. In another line of work, hybrid reward architectures (HRA) in RL have studied to model source-specific value functions for each source of reward, which is also shown to be beneficial in performance. To fully inherit the benefits of distributional RL and hybrid reward architectures, we introduce Multi-Dimensional Distributional DQN (MD3QN), which extends distributional RL to model the joint return distribution from multiple reward sources. As a by-product of joint distribution modeling, MD3QN can capture not only the randomness in returns for each source of reward, but also the rich reward correlation between the randomness of different sources. We prove the convergence for the joint distributional Bellman operator and build our empirical algorithm by minimizing the Maximum Mean Discrepancy between joint return distribution and its Bellman target. In experiments, our method accurately models the joint return distribution in environments with richly correlated reward functions, and outperforms previous RL methods utilizing multi-dimensional reward functions in the control setting.

While many real-world problems that might benefit from reinforcement learning, these problems rarely fit into the MDP mold: interacting with the environment is often expensive and specifying reward functions is challenging. Motivated by these challenges, prior work has developed data-driven approaches that learn entirely from samples from the transition dynamics and examples of high-return states. These methods typically learn a reward function from high-return states, use that reward function to label the transitions, and then apply an offline RL algorithm to these transitions. While these methods can achieve good results on many tasks, they can be complex, often requiring regularization and temporal difference updates. In this paper, we propose a method for offline, example-based control that learns an implicit model of multi-step transitions, rather than a reward function. We show that this implicit model can represent the Q-values for the example-based control problem. Across a range of state-based and image-based offline control tasks, our method outperforms baselines that use learned reward functions; additional experiments demonstrate improved robustness and scaling with dataset size.

In goal-reaching reinforcement learning (RL), the optimal value function has a particular geometry, called quasimetric structure. This paper introduces Quasimetric Reinforcement Learning (QRL), a new RL method that utilizes quasimetric models to learn optimal value functions. Distinct from prior approaches, the QRL objective is specifically designed for quasimetrics, and provides strong theoretical recovery guarantees. Empirically, we conduct thorough analyses on a discretized MountainCar environment, identifying properties of QRL and its advantages over alternatives. On offline and online goal-reaching benchmarks, QRL also demonstrates improved sample efficiency and performance, across both state-based and image-based observations.

We study the problem of cooperative multi-agent reinforcement learning with a single joint reward signal. This class of learning problems is difficult because of the often large combined action and observation spaces. In the fully centralized and decentralized approaches, we find the problem of spurious rewards and a phenomenon we call the "lazy agent" problem, which arises due to partial observability. We address these problems by training individual agents with a novel value decomposition network architecture, which learns to decompose the team value function into agent-wise value functions. We perform an experimental evaluation across a range of partially-observable multi-agent domains and show that learning such value-decompositions leads to superior results, in particular when combined with weight sharing, role information and information channels.

Off-policy learning from multistep returns is crucial for sample-efficient reinforcement learning, but counteracting off-policy bias without exacerbating variance is challenging. Classically, off-policy bias is corrected in a per-decision manner: past temporal-difference errors are re-weighted by the instantaneous Importance Sampling (IS) ratio after each action via eligibility traces. Many off-policy algorithms rely on this mechanism, along with differing protocols for cutting the IS ratios to combat the variance of the IS estimator. Unfortunately, once a trace has been fully cut, the effect cannot be reversed. This has led to the development of credit-assignment strategies that account for multiple past experiences at a time. These trajectory-aware methods have not been extensively analyzed, and their theoretical justification remains uncertain. In this paper, we propose a multistep operator that can express both per-decision and trajectory-aware methods. We prove convergence conditions for our operator in the tabular setting, establishing the first guarantees for several existing methods as well as many new ones. Finally, we introduce Recency-Bounded Importance Sampling (RBIS), which leverages trajectory awareness to perform robustly across lambda-values in an off-policy control task.

In contrast to classical reinforcement learning, distributional reinforcement learning algorithms aim to learn the distribution of returns rather than their expected value. Since the nature of the return distribution is generally unknown a priori or arbitrarily complex, a common approach finds approximations within a set of representable, parametric distributions. Typically, this involves a projection of the unconstrained distribution onto the set of simplified distributions. We argue that this projection step entails a strong inductive bias when coupled with neural networks and gradient descent, thereby profoundly impacting the generalization behavior of learned models. In order to facilitate reliable uncertainty estimation through diversity, this work studies the combination of several different projections and representations in a distributional ensemble. We establish theoretical properties of such projection ensembles and derive an algorithm that uses ensemble disagreement, measured by the average 1-Wasserstein distance, as a bonus for deep exploration. We evaluate our algorithm on the behavior suite benchmark and find that diverse projection ensembles lead to significant performance improvements over existing methods on a wide variety of tasks with the most pronounced gains in directed exploration problems.

Most offline reinforcement learning (RL) algorithms return a target policy maximizing a trade-off between (1) the expected performance gain over the behavior policy that collected the dataset, and (2) the risk stemming from the out-of-distribution-ness of the induced state-action occupancy. It follows that the performance of the target policy is strongly related to the performance of the behavior policy and, thus, the trajectory return distribution of the dataset. We show that in mixed datasets consisting of mostly low-return trajectories and minor high-return trajectories, state-of-the-art offline RL algorithms are overly restrained by low-return trajectories and fail to exploit high-performing trajectories to the fullest. To overcome this issue, we show that, in deterministic MDPs with stochastic initial states, the dataset sampling can be re-weighted to induce an artificial dataset whose behavior policy has a higher return. This re-weighted sampling strategy may be combined with any offline RL algorithm. We further analyze that the opportunity for performance improvement over the behavior policy correlates with the positive-sided variance of the returns of the trajectories in the dataset. We empirically show that while CQL, IQL, and TD3+BC achieve only a part of this potential policy improvement, these same algorithms combined with our reweighted sampling strategy fully exploit the dataset. Furthermore, we empirically demonstrate that, despite its theoretical limitation, the approach may still be efficient in stochastic environments. The code is available at https://github.com/Improbable-AI/harness-offline-rl.

Reinforcement Learning (RL) has demonstrated tremendous empirical success across numerous challenging domains. However, we lack a strong theoretical understanding of the statistical complexity of RL in environments with large state spaces, where function approximation is required for sample-efficient learning. This thesis addresses this gap by rigorously examining the statistical complexity of RL with function approximation from a learning theoretic perspective. Departing from a long history of prior work, we consider the weakest form of function approximation, called agnostic policy learning, in which the learner seeks to find the best policy in a given class Pi, with no guarantee that Pi contains an optimal policy for the underlying task. We systematically explore agnostic policy learning along three key axes: environment access -- how a learner collects data from the environment; coverage conditions -- intrinsic properties of the underlying MDP measuring the expansiveness of state-occupancy measures for policies in the class Pi, and representational conditions -- structural assumptions on the class Pi itself. Within this comprehensive framework, we (1) design new learning algorithms with theoretical guarantees and (2) characterize fundamental performance bounds of any algorithm. Our results reveal significant statistical separations that highlight the power and limitations of agnostic policy learning.

Two main challenges in Reinforcement Learning (RL) are designing appropriate reward functions and ensuring the safety of the learned policy. To address these challenges, we present a theoretical framework for Inverse Reinforcement Learning (IRL) in constrained Markov decision processes. From a convex-analytic perspective, we extend prior results on reward identifiability and generalizability to both the constrained setting and a more general class of regularizations. In particular, we show that identifiability up to potential shaping (Cao et al., 2021) is a consequence of entropy regularization and may generally no longer hold for other regularizations or in the presence of safety constraints. We also show that to ensure generalizability to new transition laws and constraints, the true reward must be identified up to a constant. Additionally, we derive a finite sample guarantee for the suboptimality of the learned rewards, and validate our results in a gridworld environment.

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.

Reinforcement learning (RL) is a general paradigm for studying intelligent behaviour, with applications ranging from artificial intelligence to psychology and economics. AIXI is a universal solution to the RL problem; it can learn any computable environment. A technical subtlety of AIXI is that it is defined using a mixture over semimeasures that need not sum to 1, rather than over proper probability measures. In this work we argue that the shortfall of a semimeasure can naturally be interpreted as the agent's estimate of the probability of its death. We formally define death for generally intelligent agents like AIXI, and prove a number of related theorems about their behaviour. Notable discoveries include that agent behaviour can change radically under positive linear transformations of the reward signal (from suicidal to dogmatically self-preserving), and that the agent's posterior belief that it will survive increases over time.

Offline reinforcement learning (RL) presents a promising approach for learning reinforced policies from offline datasets without the need for costly or unsafe interactions with the environment. However, datasets collected by humans in real-world environments are often noisy and may even be maliciously corrupted, which can significantly degrade the performance of offline RL. In this work, we first investigate the performance of current offline RL algorithms under comprehensive data corruption, including states, actions, rewards, and dynamics. Our extensive experiments reveal that implicit Q-learning (IQL) demonstrates remarkable resilience to data corruption among various offline RL algorithms. Furthermore, we conduct both empirical and theoretical analyses to understand IQL's robust performance, identifying its supervised policy learning scheme as the key factor. Despite its relative robustness, IQL still suffers from heavy-tail targets of Q functions under dynamics corruption. To tackle this challenge, we draw inspiration from robust statistics to employ the Huber loss to handle the heavy-tailedness and utilize quantile estimators to balance penalization for corrupted data and learning stability. By incorporating these simple yet effective modifications into IQL, we propose a more robust offline RL approach named Robust IQL (RIQL). Extensive experiments demonstrate that RIQL exhibits highly robust performance when subjected to diverse data corruption scenarios.

Policy gradient methods are an appealing approach in reinforcement learning because they directly optimize the cumulative reward and can straightforwardly be used with nonlinear function approximators such as neural networks. The two main challenges are the large number of samples typically required, and the difficulty of obtaining stable and steady improvement despite the nonstationarity of the incoming data. We address the first challenge by using value functions to substantially reduce the variance of policy gradient estimates at the cost of some bias, with an exponentially-weighted estimator of the advantage function that is analogous to TD(lambda). We address the second challenge by using trust region optimization procedure for both the policy and the value function, which are represented by neural networks. Our approach yields strong empirical results on highly challenging 3D locomotion tasks, learning running gaits for bipedal and quadrupedal simulated robots, and learning a policy for getting the biped to stand up from starting out lying on the ground. In contrast to a body of prior work that uses hand-crafted policy representations, our neural network policies map directly from raw kinematics to joint torques. Our algorithm is fully model-free, and the amount of simulated experience required for the learning tasks on 3D bipeds corresponds to 1-2 weeks of real time.

Reinforcement learning (RL) theory has largely focused on proving minimax sample complexity bounds. These require strategic exploration algorithms that use relatively limited function classes for representing the policy or value function. Our goal is to explain why deep RL algorithms often perform well in practice, despite using random exploration and much more expressive function classes like neural networks. Our work arrives at an explanation by showing that many stochastic MDPs can be solved by performing only a few steps of value iteration on the random policy's Q function and then acting greedily. When this is true, we find that it is possible to separate the exploration and learning components of RL, making it much easier to analyze. We introduce a new RL algorithm, SQIRL, that iteratively learns a near-optimal policy by exploring randomly to collect rollouts and then performing a limited number of steps of fitted-Q iteration over those rollouts. Any regression algorithm that satisfies basic in-distribution generalization properties can be used in SQIRL to efficiently solve common MDPs. This can explain why deep RL works, since it is empirically established that neural networks generalize well in-distribution. Furthermore, SQIRL explains why random exploration works well in practice. We leverage SQIRL to derive instance-dependent sample complexity bounds for RL that are exponential only in an "effective horizon" of lookahead and on the complexity of the class used for function approximation. Empirically, we also find that SQIRL performance strongly correlates with PPO and DQN performance in a variety of stochastic environments, supporting that our theoretical analysis is predictive of practical performance. Our code and data are available at https://github.com/cassidylaidlaw/effective-horizon.

Existing Reinforcement Learning from Verifiable Rewards (RLVR) methods, such as Group Relative Policy Optimization (GRPO), have achieved remarkable progress in improving the reasoning capabilities of Large Reasoning Models (LRMs). However, they exhibit limited exploration due to reliance on on-policy rollouts where confined to the current policy's distribution, resulting in narrow trajectory diversity. Recent approaches attempt to expand policy coverage by incorporating trajectories generated from stronger expert models, yet this reliance increases computational cost and such advaned models are often inaccessible. To address these issues, we propose In-Context Steered Policy Optimization (ICPO), a unified framework that leverages the inherent in-context learning capability of LRMs to provide expert guidance using existing datasets. ICPO introduces Mixed-Policy GRPO with Implicit Expert Forcing, which expands exploration beyond the current policy distribution without requiring advanced LRM trajectories. To further stabilize optimization, ICPO integrates Expert Region Reject Sampling to filter unreliable off-policy trajectories and Annealed Expert-Bonus Reward Shaping to balance early expert guidance with later autonomous improvement. Results demonstrate that ICPO consistently enhances reinforcement learning performance and training stability on mathematical reasoning benchmarks, revealing a scalable and effective RLVR paradigm for LRMs.

Existing theoretical studies on offline reinforcement learning (RL) mostly consider a dataset sampled directly from the target task. In practice, however, data often come from several heterogeneous but related sources. Motivated by this gap, this work aims at rigorously understanding offline RL with multiple datasets that are collected from randomly perturbed versions of the target task instead of from itself. An information-theoretic lower bound is derived, which reveals a necessary requirement on the number of involved sources in addition to that on the number of data samples. Then, a novel HetPEVI algorithm is proposed, which simultaneously considers the sample uncertainties from a finite number of data samples per data source and the source uncertainties due to a finite number of available data sources. Theoretical analyses demonstrate that HetPEVI can solve the target task as long as the data sources collectively provide a good data coverage. Moreover, HetPEVI is demonstrated to be optimal up to a polynomial factor of the horizon length. Finally, the study is extended to offline Markov games and offline robust RL, which demonstrates the generality of the proposed designs and theoretical analyses.

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.

We study the problem of nonepisodic reinforcement learning (RL) for nonlinear dynamical systems, where the system dynamics are unknown and the RL agent has to learn from a single trajectory, i.e., without resets. We propose Nonepisodic Optimistic RL (NeoRL), an approach based on the principle of optimism in the face of uncertainty. NeoRL uses well-calibrated probabilistic models and plans optimistically w.r.t. the epistemic uncertainty about the unknown dynamics. Under continuity and bounded energy assumptions on the system, we provide a first-of-its-kind regret bound of O(Gamma_T T) for general nonlinear systems with Gaussian process dynamics. We compare NeoRL to other baselines on several deep RL environments and empirically demonstrate that NeoRL achieves the optimal average cost while incurring the least regret.

Offline reinforcement learning (RL) presents an attractive paradigm for training intelligent agents without expensive online interactions. However, current approaches still struggle with complex, long-horizon sequential decision making. In this work, we introduce DEtached value learning with Action Sequence (DEAS), a simple yet effective offline RL framework that leverages action sequences for value learning. These temporally extended actions provide richer information than single-step actions and can be interpreted through the options framework via semi-Markov decision process Q-learning, enabling reduction of the effective planning horizon by considering longer sequences at once. However, directly adopting such sequences in actor-critic algorithms introduces excessive value overestimation, which we address through detached value learning that steers value estimates toward in-distribution actions that achieve high return in the offline dataset. We demonstrate that DEAS consistently outperforms baselines on complex, long-horizon tasks from OGBench and can be applied to enhance the performance of large-scale Vision-Language-Action models that predict action sequences, significantly boosting performance in both RoboCasa Kitchen simulation tasks and real-world manipulation tasks.

Effective offline RL methods require properly handling out-of-distribution actions. Implicit Q-learning (IQL) addresses this by training a Q-function using only dataset actions through a modified Bellman backup. However, it is unclear which policy actually attains the values represented by this implicitly trained Q-function. In this paper, we reinterpret IQL as an actor-critic method by generalizing the critic objective and connecting it to a behavior-regularized implicit actor. This generalization shows how the induced actor balances reward maximization and divergence from the behavior policy, with the specific loss choice determining the nature of this tradeoff. Notably, this actor can exhibit complex and multimodal characteristics, suggesting issues with the conditional Gaussian actor fit with advantage weighted regression (AWR) used in prior methods. Instead, we propose using samples from a diffusion parameterized behavior policy and weights computed from the critic to then importance sampled our intended policy. We introduce Implicit Diffusion Q-learning (IDQL), combining our general IQL critic with the policy extraction method. IDQL maintains the ease of implementation of IQL while outperforming prior offline RL methods and demonstrating robustness to hyperparameters. Code is available at https://github.com/philippe-eecs/IDQL.

Reinforcement learning (RL) is the dominant paradigm for sharpening strategic tool use capabilities of LLMs on long-horizon, sparsely-rewarded agent tasks, yet it faces a fundamental challenge of exploration-exploitation trade-off. Existing studies stimulate exploration through the lens of policy entropy, but such mechanical entropy maximization is prone to RL training instability due to the multi-turn distribution shifting. In this paper, we target the progressive exploration-exploitation balance under the guidance of the agent own experiences without succumbing to either entropy collapsing or runaway divergence. We propose SPEAR, a curriculum-based self-imitation learning (SIL) recipe for training agentic LLMs. It extends the vanilla SIL framework, where a replay buffer stores self-generated promising trajectories for off-policy update, by gradually steering the policy evolution within a well-balanced range of entropy across stages. Specifically, our approach incorporates a curriculum to manage the exploration process, utilizing intrinsic rewards to foster skill-level exploration and facilitating action-level exploration through SIL. At first, the auxiliary tool call reward plays a critical role in the accumulation of tool-use skills, enabling broad exposure to the unfamiliar distributions of the environment feedback with an upward entropy trend. As training progresses, self-imitation gets strengthened to exploit existing successful patterns from replayed experiences for comparative action-level exploration, accelerating solution iteration without unbounded entropy growth. To further stabilize training, we recalibrate the advantages of experiences in the replay buffer to address the potential policy drift. Reugularizations such as the clipping of tokens with high covariance between probability and advantage are introduced to the trajectory-level entropy control to curb over-confidence.

In this paper we introduce a new unsupervised reinforcement learning method for discovering the set of intrinsic options available to an agent. This set is learned by maximizing the number of different states an agent can reliably reach, as measured by the mutual information between the set of options and option termination states. To this end, we instantiate two policy gradient based algorithms, one that creates an explicit embedding space of options and one that represents options implicitly. The algorithms also provide an explicit measure of empowerment in a given state that can be used by an empowerment maximizing agent. The algorithm scales well with function approximation and we demonstrate the applicability of the algorithm on a range of tasks.

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.

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.

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/.

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 (RL) is a popular machine learning paradigm where intelligent agents interact with the environment to fulfill a long-term goal. Driven by the resurgence of deep learning, Deep RL (DRL) has witnessed great success over a wide spectrum of complex control tasks. Despite the encouraging results achieved, the deep neural network-based backbone is widely deemed as a black box that impedes practitioners to trust and employ trained agents in realistic scenarios where high security and reliability are essential. To alleviate this issue, a large volume of literature devoted to shedding light on the inner workings of the intelligent agents has been proposed, by constructing intrinsic interpretability or post-hoc explainability. In this survey, we provide a comprehensive review of existing works on eXplainable RL (XRL) and introduce a new taxonomy where prior works are clearly categorized into model-explaining, reward-explaining, state-explaining, and task-explaining methods. We also review and highlight RL methods that conversely leverage human knowledge to promote learning efficiency and performance of agents while this kind of method is often ignored in XRL field. Some challenges and opportunities in XRL are discussed. This survey intends to provide a high-level summarization of XRL and to motivate future research on more effective XRL solutions. Corresponding open source codes are collected and categorized at https://github.com/Plankson/awesome-explainable-reinforcement-learning.

This study focuses on the topic of offline preference-based reinforcement learning (PbRL), a variant of conventional reinforcement learning that dispenses with the need for online interaction or specification of reward functions. Instead, the agent is provided with fixed offline trajectories and human preferences between pairs of trajectories to extract the dynamics and task information, respectively. Since the dynamics and task information are orthogonal, a naive approach would involve using preference-based reward learning followed by an off-the-shelf offline RL algorithm. However, this requires the separate learning of a scalar reward function, which is assumed to be an information bottleneck of the learning process. To address this issue, we propose the offline preference-guided policy optimization (OPPO) paradigm, which models offline trajectories and preferences in a one-step process, eliminating the need for separately learning a reward function. OPPO achieves this by introducing an offline hindsight information matching objective for optimizing a contextual policy and a preference modeling objective for finding the optimal context. OPPO further integrates a well-performing decision policy by optimizing the two objectives iteratively. Our empirical results demonstrate that OPPO effectively models offline preferences and outperforms prior competing baselines, including offline RL algorithms performed over either true or pseudo reward function specifications. Our code is available on the project website: https://sites.google.com/view/oppo-icml-2023 .

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.

In many real-world multi-agent cooperative tasks, due to high cost and risk, agents cannot continuously interact with the environment and collect experiences during learning, but have to learn from offline datasets. However, the transition dynamics in the dataset of each agent can be much different from the ones induced by the learned policies of other agents in execution, creating large errors in value estimates. Consequently, agents learn uncoordinated low-performing policies. In this paper, we propose a framework for offline decentralized multi-agent reinforcement learning, which exploits value deviation and transition normalization to deliberately modify the transition probabilities. Value deviation optimistically increases the transition probabilities of high-value next states, and transition normalization normalizes the transition probabilities of next states. They together enable agents to learn high-performing and coordinated policies. Theoretically, we prove the convergence of Q-learning under the altered non-stationary transition dynamics. Empirically, we show that the framework can be easily built on many existing offline reinforcement learning algorithms and achieve substantial improvement in a variety of multi-agent tasks.

In this work, we build on recent advances in distributional reinforcement learning to give a generally applicable, flexible, and state-of-the-art distributional variant of DQN. We achieve this by using quantile regression to approximate the full quantile function for the state-action return distribution. By reparameterizing a distribution over the sample space, this yields an implicitly defined return distribution and gives rise to a large class of risk-sensitive policies. We demonstrate improved performance on the 57 Atari 2600 games in the ALE, and use our algorithm's implicitly defined distributions to study the effects of risk-sensitive policies in Atari games.

Most value function learning algorithms in reinforcement learning are based on the mean squared (projected) Bellman error. However, squared errors are known to be sensitive to outliers, both skewing the solution of the objective and resulting in high-magnitude and high-variance gradients. To control these high-magnitude updates, typical strategies in RL involve clipping gradients, clipping rewards, rescaling rewards, or clipping errors. While these strategies appear to be related to robust losses -- like the Huber loss -- they are built on semi-gradient update rules which do not minimize a known loss. In this work, we build on recent insights reformulating squared Bellman errors as a saddlepoint optimization problem and propose a saddlepoint reformulation for a Huber Bellman error and Absolute Bellman error. We start from a formalization of robust losses, then derive sound gradient-based approaches to minimize these losses in both the online off-policy prediction and control settings. We characterize the solutions of the robust losses, providing insight into the problem settings where the robust losses define notably better solutions than the mean squared Bellman error. Finally, we show that the resulting gradient-based algorithms are more stable, for both prediction and control, with less sensitivity to meta-parameters.

While reinforcement learning (RL) has achieved great success in acquiring complex skills solely from environmental interactions, it assumes that resets to the initial state are readily available at the end of each episode. Such an assumption hinders the autonomous learning of embodied agents due to the time-consuming and cumbersome workarounds for resetting in the physical world. Hence, there has been a growing interest in autonomous RL (ARL) methods that are capable of learning from non-episodic interactions. However, existing works on ARL are limited by their reliance on prior data and are unable to learn in environments where task-relevant interactions are sparse. In contrast, we propose a demonstration-free ARL algorithm via Implicit and Bi-directional Curriculum (IBC). With an auxiliary agent that is conditionally activated upon learning progress and a bidirectional goal curriculum based on optimal transport, our method outperforms previous methods, even the ones that leverage demonstrations.

Actor-critic algorithms have become a cornerstone in reinforcement learning (RL), leveraging the strengths of both policy-based and value-based methods. Despite recent progress in understanding their statistical efficiency, no existing work has successfully learned an epsilon-optimal policy with a sample complexity of O(1/epsilon^2) trajectories with general function approximation when strategic exploration is necessary. We address this open problem by introducing a novel actor-critic algorithm that attains a sample-complexity of O(dH^5 log|A|/epsilon^2 + d H^4 log|F|/ epsilon^2) trajectories, and accompanying T regret when the Bellman eluder dimension d does not increase with T at more than a log T rate. Here, F is the critic function class, A is the action space, and H is the horizon in the finite horizon MDP setting. Our algorithm integrates optimism, off-policy critic estimation targeting the optimal Q-function, and rare-switching policy resets. We extend this to the setting of Hybrid RL, showing that initializing the critic with offline data yields sample efficiency gains compared to purely offline or online RL. Further, utilizing access to offline data, we provide a non-optimistic provably efficient actor-critic algorithm that only additionally requires N_{off} geq c_{off}^*dH^4/epsilon^2 in exchange for omitting optimism, where c_{off}^* is the single-policy concentrability coefficient and N_{off} is the number of offline samples. This addresses another open problem in the literature. We further provide numerical experiments to support our theoretical findings.

Reinforcement learning (RL) has increasingly been applied to solve real-world planning problems, with progress in handling large state spaces and time horizons. However, a key bottleneck in many domains is that RL methods cannot accommodate large, combinatorially structured action spaces. In such settings, even representing the set of feasible actions at a single step may require a complex discrete optimization formulation. We leverage recent advances in embedding trained neural networks into optimization problems to propose SEQUOIA, an RL algorithm that directly optimizes for long-term reward over the feasible action space. Our approach embeds a Q-network into a mixed-integer program to select a combinatorial action in each timestep. Here, we focus on planning over restless bandits, a class of planning problems which capture many real-world examples of sequential decision making. We introduce coRMAB, a broader class of restless bandits with combinatorial actions that cannot be decoupled across the arms of the restless bandit, requiring direct solving over the joint, exponentially large action space. We empirically validate SEQUOIA on four novel restless bandit problems with combinatorial constraints: multiple interventions, path constraints, bipartite matching, and capacity constraints. Our approach significantly outperforms existing methods -- which cannot address sequential planning and combinatorial selection simultaneously -- by an average of 24.8\% on these difficult instances.

The Rubiks Cube, with its vast state space and sparse reward structure, presents a significant challenge for reinforcement learning (RL) due to the difficulty of reaching rewarded states. Previous research addressed this by propagating cost-to-go estimates from the solved state and incorporating search techniques. These approaches differ from human strategies that start from fully scrambled cubes, which can be tricky for solving a general sparse-reward problem. In this paper, we introduce a novel RL algorithm using policy gradient methods to solve the Rubiks Cube without relying on near solved-state sampling. Our approach employs a neural network to predict cost patterns between states, allowing the agent to learn directly from scrambled states. Our method was tested on the 2x2x2 Rubiks Cube, where the cube was scrambled 50,000 times, and the model successfully solved it in over 99.4% of cases. Notably, this result was achieved using only the policy network without relying on tree search as in previous methods, demonstrating its effectiveness and potential for broader applications in sparse-reward problems.

The application of Reinforcement Learning (RL) in real world environments can be expensive or risky due to sub-optimal policies during training. In Offline RL, this problem is avoided since interactions with an environment are prohibited. Policies are learned from a given dataset, which solely determines their performance. Despite this fact, how dataset characteristics influence Offline RL algorithms is still hardly investigated. The dataset characteristics are determined by the behavioral policy that samples this dataset. Therefore, we define characteristics of behavioral policies as exploratory for yielding high expected information in their interaction with the Markov Decision Process (MDP) and as exploitative for having high expected return. We implement two corresponding empirical measures for the datasets sampled by the behavioral policy in deterministic MDPs. The first empirical measure SACo is defined by the normalized unique state-action pairs and captures exploration. The second empirical measure TQ is defined by the normalized average trajectory return and captures exploitation. Empirical evaluations show the effectiveness of TQ and SACo. In large-scale experiments using our proposed measures, we show that the unconstrained off-policy Deep Q-Network family requires datasets with high SACo to find a good policy. Furthermore, experiments show that policy constraint algorithms perform well on datasets with high TQ and SACo. Finally, the experiments show, that purely dataset-constrained Behavioral Cloning performs competitively to the best Offline RL algorithms for datasets with high TQ.

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.

In reinforcement learning (RL), function approximation errors are known to easily lead to the Q-value overestimations, thus greatly reducing policy performance. This paper presents a distributional soft actor-critic (DSAC) algorithm, which is an off-policy RL method for continuous control setting, to improve the policy performance by mitigating Q-value overestimations. We first discover in theory that learning a distribution function of state-action returns can effectively mitigate Q-value overestimations because it is capable of adaptively adjusting the update stepsize of the Q-value function. Then, a distributional soft policy iteration (DSPI) framework is developed by embedding the return distribution function into maximum entropy RL. Finally, we present a deep off-policy actor-critic variant of DSPI, called DSAC, which directly learns a continuous return distribution by keeping the variance of the state-action returns within a reasonable range to address exploding and vanishing gradient problems. We evaluate DSAC on the suite of MuJoCo continuous control tasks, achieving the state-of-the-art performance.

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.

Human intelligence involves metacognitive abilities like self-regulation, recognizing limitations, and seeking assistance only when needed. While LLM Agents excel in many domains, they often lack this awareness. Overconfident agents risk catastrophic failures, while those that seek help excessively hinder efficiency. A key challenge is enabling agents with a limited intervention budget C is to decide when to request assistance. In this paper, we propose an offline framework that trains a "helper" policy to request interventions, such as more powerful models or test-time compute, by combining LLM-based process reward models (PRMs) with tabular reinforcement learning. Using state transitions collected offline, we score optimal intervention timing with PRMs and train the helper model on these labeled trajectories. This offline approach significantly reduces costly intervention calls during training. Furthermore, the integration of PRMs with tabular RL enhances robustness to off-policy data while avoiding the inefficiencies of deep RL. We empirically find that our method delivers optimal helper behavior.

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.

Intrinsic reward shaping has emerged as a prevalent approach to solving hard-exploration and sparse-rewards environments in reinforcement learning (RL). While single intrinsic rewards, such as curiosity-driven or novelty-based methods, have shown effectiveness, they often limit the diversity and efficiency of exploration. Moreover, the potential and principle of combining multiple intrinsic rewards remains insufficiently explored. To address this gap, we introduce HIRE (Hybrid Intrinsic REward), a flexible and elegant framework for creating hybrid intrinsic rewards through deliberate fusion strategies. With HIRE, we conduct a systematic analysis of the application of hybrid intrinsic rewards in both general and unsupervised RL across multiple benchmarks. Extensive experiments demonstrate that HIRE can significantly enhance exploration efficiency and diversity, as well as skill acquisition in complex and dynamic settings.

Automatically synthesizing dense rewards from natural language descriptions is a promising paradigm in reinforcement learning (RL), with applications to sparse reward problems, open-ended exploration, and hierarchical skill design. Recent works have made promising steps by exploiting the prior knowledge of large language models (LLMs). However, these approaches suffer from important limitations: they are either not scalable to problems requiring billions of environment samples, due to requiring LLM annotations for each observation, or they require a diverse offline dataset, which may not exist or be impossible to collect. In this work, we address these limitations through a combination of algorithmic and systems-level contributions. We propose \oni, a distributed architecture that simultaneously learns an RL policy and an intrinsic reward function using LLM feedback. Our approach annotates the agent's collected experience via an asynchronous LLM server, which is then distilled into an intrinsic reward model. We explore a range of algorithmic choices for reward modeling with varying complexity, including hashing, classification, and ranking models. By studying their relative tradeoffs, we shed light on questions regarding intrinsic reward design for sparse reward problems. Our approach achieves state-of-the-art performance across a range of challenging, sparse reward tasks from the NetHack Learning Environment in a simple unified process, solely using the agent's gathered experience, without requiring external datasets. We make our code available at https://github.com/facebookresearch/oni.

We provide a theoretical framework for Reinforcement Learning with Human Feedback (RLHF). Our analysis shows that when the true reward function is linear, the widely used maximum likelihood estimator (MLE) converges under both the Bradley-Terry-Luce (BTL) model and the Plackett-Luce (PL) model. However, we show that when training a policy based on the learned reward model, MLE fails while a pessimistic MLE provides policies with improved performance under certain coverage assumptions. Additionally, we demonstrate that under the PL model, the true MLE and an alternative MLE that splits the K-wise comparison into pairwise comparisons both converge. Moreover, the true MLE is asymptotically more efficient. Our results validate the empirical success of existing RLHF algorithms in InstructGPT and provide new insights for algorithm design. Furthermore, our results unify the problem of RLHF and max-entropy Inverse Reinforcement Learning (IRL), and provide the first sample complexity bound for max-entropy IRL.

Reinforcement learning (RL) has demonstrated immense potential in advancing artificial general intelligence, agentic intelligence, and embodied intelligence. However, the inherent heterogeneity and dynamicity of RL workflows often lead to low hardware utilization and slow training on existing systems. In this paper, we present RLinf, a high-performance RL training system based on our key observation that the major roadblock to efficient RL training lies in system flexibility. To maximize flexibility and efficiency, RLinf is built atop a novel RL system design paradigm called macro-to-micro flow transformation (M2Flow), which automatically breaks down high-level, easy-to-compose RL workflows at both the temporal and spatial dimensions, and recomposes them into optimized execution flows. Supported by RLinf worker's adaptive communication capability, we devise context switching and elastic pipelining to realize M2Flow transformation, and a profiling-guided scheduling policy to generate optimal execution plans. Extensive evaluations on both reasoning RL and embodied RL tasks demonstrate that RLinf consistently outperforms state-of-the-art systems, achieving 1.1x-2.13x speedup in end-to-end training throughput.

This paper introduces PG-Rainbow, a novel algorithm that incorporates a distributional reinforcement learning framework with a policy gradient algorithm. Existing policy gradient methods are sample inefficient and rely on the mean of returns when calculating the state-action value function, neglecting the distributional nature of returns in reinforcement learning tasks. To address this issue, we use an Implicit Quantile Network that provides the quantile information of the distribution of rewards to the critic network of the Proximal Policy Optimization algorithm. We show empirical results that through the integration of reward distribution information into the policy network, the policy agent acquires enhanced capabilities to comprehensively evaluate the consequences of potential actions in a given state, facilitating more sophisticated and informed decision-making processes. We evaluate the performance of the proposed algorithm in the Atari-2600 game suite, simulated via the Arcade Learning Environment (ALE).

One of the main challenges in reinforcement learning (RL) is generalisation. In typical deep RL methods this is achieved by approximating the optimal value function with a low-dimensional representation using a deep network. While this approach works well in many domains, in domains where the optimal value function cannot easily be reduced to a low-dimensional representation, learning can be very slow and unstable. This paper contributes towards tackling such challenging domains, by proposing a new method, called Hybrid Reward Architecture (HRA). HRA takes as input a decomposed reward function and learns a separate value function for each component reward function. Because each component typically only depends on a subset of all features, the corresponding value function can be approximated more easily by a low-dimensional representation, enabling more effective learning. We demonstrate HRA on a toy-problem and the Atari game Ms. Pac-Man, where HRA achieves above-human performance.

Deep reinforcement learning (RL) methods generally engage in exploratory behavior through noise injection in the action space. An alternative is to add noise directly to the agent's parameters, which can lead to more consistent exploration and a richer set of behaviors. Methods such as evolutionary strategies use parameter perturbations, but discard all temporal structure in the process and require significantly more samples. Combining parameter noise with traditional RL methods allows to combine the best of both worlds. We demonstrate that both off- and on-policy methods benefit from this approach through experimental comparison of DQN, DDPG, and TRPO on high-dimensional discrete action environments as well as continuous control tasks. Our results show that RL with parameter noise learns more efficiently than traditional RL with action space noise and evolutionary strategies individually.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a crucial paradigm for incentivizing reasoning capabilities in Large Language Models (LLMs). Due to vast state-action spaces and reward sparsity in reasoning tasks, existing methods often struggle with deficient exploration and poor sample efficiency. In the paper, we propose DIVER (Diversity-Incentivized Exploration for VersatilE Reasoning), an innovative framework that highlights the pivotal role of global sequence-level diversity to incentivize deep exploration for versatile reasoning. We first conduct a primary empirical study to reveal a strong positive correlation between global diversity and reasoning capacity. Building on this insight, we introduce global diversity incentives as an intrinsic reward to promote deep exploration in a semantically structured space. Incorporating the intrinsic reward, we develop a potential-based reward shaping mechanism to preserve optimal policy invariance and design simple heuristics to mitigate possible reward hacking. Experimental results show that DIVER outperforms competitive RLVR baselines with various exploration strategies on both in-domain and out-of-domain tasks, excelling in both Pass@1 and Pass@k evaluations. Our code is available at https://github.com/NJU-RL/DIVER.

In this work, we study the simple yet universally applicable case of reward shaping in value-based Deep Reinforcement Learning (DRL). We show that reward shifting in the form of the linear transformation is equivalent to changing the initialization of the Q-function in function approximation. Based on such an equivalence, we bring the key insight that a positive reward shifting leads to conservative exploitation, while a negative reward shifting leads to curiosity-driven exploration. Accordingly, conservative exploitation improves offline RL value estimation, and optimistic value estimation improves exploration for online RL. We validate our insight on a range of RL tasks and show its improvement over baselines: (1) In offline RL, the conservative exploitation leads to improved performance based on off-the-shelf algorithms; (2) In online continuous control, multiple value functions with different shifting constants can be used to tackle the exploration-exploitation dilemma for better sample efficiency; (3) In discrete control tasks, a negative reward shifting yields an improvement over the curiosity-based exploration method.

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.

Large language models (LLMs) have shown promise in performing complex multi-step reasoning, yet they continue to struggle with mathematical reasoning, often making systematic errors. A promising solution is reinforcement learning (RL) guided by reward models, particularly those focusing on process rewards, which score each intermediate step rather than solely evaluating the final outcome. This approach is more effective at guiding policy models towards correct reasoning trajectories. In this work, we propose an entropy-regularized process reward model (ER-PRM) that integrates KL-regularized Markov Decision Processes (MDP) to balance policy optimization with the need to prevent the policy from shifting too far from its initial distribution. We derive a novel reward construction method based on the theoretical results. Our theoretical analysis shows that we could derive the optimal reward model from the initial policy sampling. Our empirical experiments on the MATH and GSM8K benchmarks demonstrate that ER-PRM consistently outperforms existing process reward models, achieving 1% improvement on GSM8K and 2-3% improvement on MATH under best-of-N evaluation, and more than 1% improvement under RLHF. These results highlight the efficacy of entropy-regularization in enhancing LLMs' reasoning capabilities.

Reinforcement Learning (RL) has emerged as a transformative approach for aligning and enhancing Large Language Models (LLMs), addressing critical challenges in instruction following, ethical alignment, and reasoning capabilities. This survey offers a comprehensive foundation on the integration of RL with language models, highlighting prominent algorithms such as Proximal Policy Optimization (PPO), Q-Learning, and Actor-Critic methods. Additionally, it provides an extensive technical overview of RL techniques specifically tailored for LLMs, including foundational methods like Reinforcement Learning from Human Feedback (RLHF) and AI Feedback (RLAIF), as well as advanced strategies such as Direct Preference Optimization (DPO) and Group Relative Policy Optimization (GRPO). We systematically analyze their applications across domains, i.e., from code generation to tool-augmented reasoning. We also present a comparative taxonomy based on reward modeling, feedback mechanisms, and optimization strategies. Our evaluation highlights key trends. RLHF remains dominant for alignment, and outcome-based RL such as RLVR significantly improves stepwise reasoning. However, persistent challenges such as reward hacking, computational costs, and scalable feedback collection underscore the need for continued innovation. We further discuss emerging directions, including hybrid RL algorithms, verifier-guided training, and multi-objective alignment frameworks. This survey serves as a roadmap for researchers advancing RL-driven LLM development, balancing capability enhancement with safety and scalability.

We study how to learn ε-optimal strategies in zero-sum imperfect information games (IIG) with trajectory feedback. In this setting, players update their policies sequentially based on their observations over a fixed number of episodes, denoted by T. Existing procedures suffer from high variance due to the use of importance sampling over sequences of actions (Steinberger et al., 2020; McAleer et al., 2022). To reduce this variance, we consider a fixed sampling approach, where players still update their policies over time, but with observations obtained through a given fixed sampling policy. Our approach is based on an adaptive Online Mirror Descent (OMD) algorithm that applies OMD locally to each information set, using individually decreasing learning rates and a regularized loss. We show that this approach guarantees a convergence rate of mathcal{O}(T^{-1/2}) with high probability and has a near-optimal dependence on the game parameters when applied with the best theoretical choices of learning rates and sampling policies. To achieve these results, we generalize the notion of OMD stabilization, allowing for time-varying regularization with convex increments.

Diffusion models have emerged as powerful generative tools across various domains, yet tailoring pre-trained models to exhibit specific desirable properties remains challenging. While reinforcement learning (RL) offers a promising solution,current methods struggle to simultaneously achieve stable, efficient fine-tuning and support non-differentiable rewards. Furthermore, their reliance on sparse rewards provides inadequate supervision during intermediate steps, often resulting in suboptimal generation quality. To address these limitations, dense and differentiable signals are required throughout the diffusion process. Hence, we propose VAlue-based Reinforced Diffusion (VARD): a novel approach that first learns a value function predicting expection of rewards from intermediate states, and subsequently uses this value function with KL regularization to provide dense supervision throughout the generation process. Our method maintains proximity to the pretrained model while enabling effective and stable training via backpropagation. Experimental results demonstrate that our approach facilitates better trajectory guidance, improves training efficiency and extends the applicability of RL to diffusion models optimized for complex, non-differentiable reward functions.

Stateful policies play an important role in reinforcement learning, such as handling partially observable environments, enhancing robustness, or imposing an inductive bias directly into the policy structure. The conventional method for training stateful policies is Backpropagation Through Time (BPTT), which comes with significant drawbacks, such as slow training due to sequential gradient propagation and the occurrence of vanishing or exploding gradients. The gradient is often truncated to address these issues, resulting in a biased policy update. We present a novel approach for training stateful policies by decomposing the latter into a stochastic internal state kernel and a stateless policy, jointly optimized by following the stateful policy gradient. We introduce different versions of the stateful policy gradient theorem, enabling us to easily instantiate stateful variants of popular reinforcement learning and imitation learning algorithms. Furthermore, we provide a theoretical analysis of our new gradient estimator and compare it with BPTT. We evaluate our approach on complex continuous control tasks, e.g., humanoid locomotion, and demonstrate that our gradient estimator scales effectively with task complexity while offering a faster and simpler alternative to BPTT.

In this work, we investigate the application of Taylor expansions in reinforcement learning. In particular, we propose Taylor expansion policy optimization, a policy optimization formalism that generalizes prior work (e.g., TRPO) as a first-order special case. We also show that Taylor expansions intimately relate to off-policy evaluation. Finally, we show that this new formulation entails modifications which improve the performance of several state-of-the-art distributed algorithms.

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.

Designing control policies whose performance level is guaranteed to remain above a given threshold in a span of environments is a critical feature for the adoption of reinforcement learning (RL) in real-world applications. The search for such robust policies is a notoriously difficult problem, related to the so-called dynamic model of transition function uncertainty, where the environment dynamics are allowed to change at each time step. But in practical cases, one is rather interested in robustness to a span of static transition models throughout interaction episodes. The static model is known to be harder to solve than the dynamic one, and seminal algorithms, such as robust value iteration, as well as most recent works on deep robust RL, build upon the dynamic model. In this work, we propose to revisit the static model. We suggest an analysis of why solving the static model under some mild hypotheses is a reasonable endeavor, based on an equivalence with the dynamic model, and formalize the general intuition that robust MDPs can be solved by tackling a series of static problems. We introduce a generic meta-algorithm called IWOCS, which incrementally identifies worst-case transition models so as to guide the search for a robust policy. Discussion on IWOCS sheds light on new ways to decouple policy optimization and adversarial transition functions and opens new perspectives for analysis. We derive a deep RL version of IWOCS and demonstrate it is competitive with state-of-the-art algorithms on classical benchmarks.

Exploration remains a critical challenge in online reinforcement learning, as an agent must effectively explore unknown environments to achieve high returns. Currently, the main exploration algorithms are primarily count-based methods and curiosity-based methods, with prediction-error methods being a prominent example. In this paper, we propose a novel method called Random Distribution Distillation (RDD), which samples the output of a target network from a normal distribution. RDD facilitates a more extensive exploration by explicitly treating the difference between the prediction network and the target network as an intrinsic reward. Furthermore, by introducing randomness into the output of the target network for a given state and modeling it as a sample from a normal distribution, intrinsic rewards are bounded by two key components: a pseudo-count term ensuring proper exploration decay and a discrepancy term accounting for predictor convergence. We demonstrate that RDD effectively unifies both count-based and prediction-error approaches. It retains the advantages of prediction-error methods in high-dimensional spaces, while also implementing an intrinsic reward decay mode akin to the pseudo-count method. In the experimental section, RDD is compared with more advanced methods in a series of environments. Both theoretical analysis and experimental results confirm the effectiveness of our approach in improving online exploration for reinforcement learning tasks.

Reinforcement learning (RL) for continuous control typically employs distributions whose support covers the entire action space. In this work, we investigate the colloquially known phenomenon that trained agents often prefer actions at the boundaries of that space. We draw theoretical connections to the emergence of bang-bang behavior in optimal control, and provide extensive empirical evaluation across a variety of recent RL algorithms. We replace the normal Gaussian by a Bernoulli distribution that solely considers the extremes along each action dimension - a bang-bang controller. Surprisingly, this achieves state-of-the-art performance on several continuous control benchmarks - in contrast to robotic hardware, where energy and maintenance cost affect controller choices. Since exploration, learning,and the final solution are entangled in RL, we provide additional imitation learning experiments to reduce the impact of exploration on our analysis. Finally, we show that our observations generalize to environments that aim to model real-world challenges and evaluate factors to mitigate the emergence of bang-bang solutions. Our findings emphasize challenges for benchmarking continuous control algorithms, particularly in light of potential real-world applications.

Reinforcement Learning with Verifiable Reward (RLVR) has significantly advanced the complex reasoning abilities of Large Language Models (LLMs). However, it struggles to break through the inherent capability boundaries of the base LLM, due to its essentially on-policy strategy coupled with LLM's immense action space and sparse reward. Critically, RLVR can lead to the capability boundary collapse, narrowing the LLM's problem-solving scope. To address this problem, we propose RL-PLUS, a novel hybrid-policy optimization approach for LLMs that synergizes internal exploitation with external data to achieve stronger reasoning capabilities and surpass the boundaries of base models. RL-PLUS integrates two core components, i.e., Multiple Importance Sampling to address distributional mismatch from external data, and Exploration-Based Advantage Function to guide the model towards high-value, unexplored reasoning paths. We provide both theoretical analysis and extensive experiments to demonstrate the superiority and generalizability of our approach. Compared with existing RLVR methods, RL-PLUS achieves 1) state-of-the-art performance on six math reasoning benchmarks; 2) superior performance on six out-of-distribution reasoning tasks; 3) consistent and significant gains across diverse model families, with average relative improvements up to 69.2\%. Moreover, the analysis of Pass@k curves indicates that RL-PLUS effectively resolves the capability boundary collapse problem.

Sequential decision making, commonly formalized as Markov Decision Process (MDP) optimization, is a important challenge in artificial intelligence. Two key approaches to this problem are reinforcement learning (RL) and planning. This paper presents a survey of the integration of both fields, better known as model-based reinforcement learning. Model-based RL has two main steps. First, we systematically cover approaches to dynamics model learning, including challenges like dealing with stochasticity, uncertainty, partial observability, and temporal abstraction. Second, we present a systematic categorization of planning-learning integration, including aspects like: where to start planning, what budgets to allocate to planning and real data collection, how to plan, and how to integrate planning in the learning and acting loop. After these two sections, we also discuss implicit model-based RL as an end-to-end alternative for model learning and planning, and we cover the potential benefits of model-based RL. Along the way, the survey also draws connections to several related RL fields, like hierarchical RL and transfer learning. Altogether, the survey presents a broad conceptual overview of the combination of planning and learning for MDP optimization.

A common pipeline in learning-based control is to iteratively estimate a model of system dynamics, and apply a trajectory optimization algorithm - e.g.~iLQR - on the learned model to minimize a target cost. This paper conducts a rigorous analysis of a simplified variant of this strategy for general nonlinear systems. We analyze an algorithm which iterates between estimating local linear models of nonlinear system dynamics and performing iLQR-like policy updates. We demonstrate that this algorithm attains sample complexity polynomial in relevant problem parameters, and, by synthesizing locally stabilizing gains, overcomes exponential dependence in problem horizon. Experimental results validate the performance of our algorithm, and compare to natural deep-learning baselines.

In problem-solving, we humans can come up with multiple novel solutions to the same problem. However, reinforcement learning algorithms can only produce a set of monotonous policies that maximize the cumulative reward but lack diversity and novelty. In this work, we address the problem of generating novel policies in reinforcement learning tasks. Instead of following the multi-objective framework used in existing methods, we propose to rethink the problem under a novel perspective of constrained optimization. We first introduce a new metric to evaluate the difference between policies and then design two practical novel policy generation methods following the new perspective. The two proposed methods, namely the Constrained Task Novel Bisector (CTNB) and the Interior Policy Differentiation (IPD), are derived from the feasible direction method and the interior point method commonly known in the constrained optimization literature. Experimental comparisons on the MuJoCo control suite show our methods can achieve substantial improvement over previous novelty-seeking methods in terms of both the novelty of policies and their performances in the primal task.

Off-policy reinforcement learning (RL) has proven to be a powerful framework for guiding agents' actions in environments with stochastic rewards and unknown or noisy state dynamics. In many real-world settings, these agents must operate in multiple environments, each with slightly different dynamics. For example, we may be interested in developing policies to guide medical treatment for patients with and without a given disease, or policies to navigate curriculum design for students with and without a learning disability. Here, we introduce nested policy fitted Q-iteration (NFQI), an RL framework that finds optimal policies in environments that exhibit such a structure. Our approach develops a nested Q-value function that takes advantage of the shared structure between two groups of observations from two separate environments while allowing their policies to be distinct from one another. We find that NFQI yields policies that rely on relevant features and perform at least as well as a policy that does not consider group structure. We demonstrate NFQI's performance using an OpenAI Gym environment and a clinical decision making RL task. Our results suggest that NFQI can develop policies that are better suited to many real-world clinical environments.

Model-based reinforcement learning methods often use learning only for the purpose of estimating an approximate dynamics model, offloading the rest of the decision-making work to classical trajectory optimizers. While conceptually simple, this combination has a number of empirical shortcomings, suggesting that learned models may not be well-suited to standard trajectory optimization. In this paper, we consider what it would look like to fold as much of the trajectory optimization pipeline as possible into the modeling problem, such that sampling from the model and planning with it become nearly identical. The core of our technical approach lies in a diffusion probabilistic model that plans by iteratively denoising trajectories. We show how classifier-guided sampling and image inpainting can be reinterpreted as coherent planning strategies, explore the unusual and useful properties of diffusion-based planning methods, and demonstrate the effectiveness of our framework in control settings that emphasize long-horizon decision-making and test-time flexibility.

The purpose of offline multi-task reinforcement learning (MTRL) is to develop a unified policy applicable to diverse tasks without the need for online environmental interaction. Recent advancements approach this through sequence modeling, leveraging the Transformer architecture's scalability and the benefits of parameter sharing to exploit task similarities. However, variations in task content and complexity pose significant challenges in policy formulation, necessitating judicious parameter sharing and management of conflicting gradients for optimal policy performance. In this work, we introduce the Harmony Multi-Task Decision Transformer (HarmoDT), a novel solution designed to identify an optimal harmony subspace of parameters for each task. We approach this as a bi-level optimization problem, employing a meta-learning framework that leverages gradient-based techniques. The upper level of this framework is dedicated to learning a task-specific mask that delineates the harmony subspace, while the inner level focuses on updating parameters to enhance the overall performance of the unified policy. Empirical evaluations on a series of benchmarks demonstrate the superiority of HarmoDT, verifying the effectiveness of our approach.

Offline preference-based reinforcement learning (PbRL) typically operates in two phases: first, use human preferences to learn a reward model and annotate rewards for a reward-free offline dataset; second, learn a policy by optimizing the learned reward via offline RL. However, accurately modeling step-wise rewards from trajectory-level preference feedback presents inherent challenges. The reward bias introduced, particularly the overestimation of predicted rewards, leads to optimistic trajectory stitching, which undermines the pessimism mechanism critical to the offline RL phase. To address this challenge, we propose In-Dataset Trajectory Return Regularization (DTR) for offline PbRL, which leverages conditional sequence modeling to mitigate the risk of learning inaccurate trajectory stitching under reward bias. Specifically, DTR employs Decision Transformer and TD-Learning to strike a balance between maintaining fidelity to the behavior policy with high in-dataset trajectory returns and selecting optimal actions based on high reward labels. Additionally, we introduce an ensemble normalization technique that effectively integrates multiple reward models, balancing the tradeoff between reward differentiation and accuracy. Empirical evaluations on various benchmarks demonstrate the superiority of DTR over other state-of-the-art baselines.

In reinforcement learning (RL), there are two major settings for interacting with the environment: online and offline. Online methods explore the environment at significant time cost, and offline methods efficiently obtain reward signals by sacrificing exploration capability. We propose semi-offline RL, a novel paradigm that smoothly transits from offline to online settings, balances exploration capability and training cost, and provides a theoretical foundation for comparing different RL settings. Based on the semi-offline formulation, we present the RL setting that is optimal in terms of optimization cost, asymptotic error, and overfitting error bound. Extensive experiments show that our semi-offline approach is efficient and yields comparable or often better performance compared with state-of-the-art methods.

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.

Reinforcement learning (RL) provides a theoretical framework for continuously improving an agent's behavior via trial and error. However, efficiently learning policies from scratch can be very difficult, particularly for tasks with exploration challenges. In such settings, it might be desirable to initialize RL with an existing policy, offline data, or demonstrations. However, naively performing such initialization in RL often works poorly, especially for value-based methods. In this paper, we present a meta algorithm that can use offline data, demonstrations, or a pre-existing policy to initialize an RL policy, and is compatible with any RL approach. In particular, we propose Jump-Start Reinforcement Learning (JSRL), an algorithm that employs two policies to solve tasks: a guide-policy, and an exploration-policy. By using the guide-policy to form a curriculum of starting states for the exploration-policy, we are able to efficiently improve performance on a set of simulated robotic tasks. We show via experiments that JSRL is able to significantly outperform existing imitation and reinforcement learning algorithms, particularly in the small-data regime. In addition, we provide an upper bound on the sample complexity of JSRL and show that with the help of a guide-policy, one can improve the sample complexity for non-optimism exploration methods from exponential in horizon to polynomial.

We introduce distributional dynamic programming (DP) methods for optimizing statistical functionals of the return distribution, with standard reinforcement learning as a special case. Previous distributional DP methods could optimize the same class of expected utilities as classic DP. To go beyond expected utilities, we combine distributional DP with stock augmentation, a technique previously introduced for classic DP in the context of risk-sensitive RL, where the MDP state is augmented with a statistic of the rewards obtained so far (since the first time step). We find that a number of recently studied problems can be formulated as stock-augmented return distribution optimization, and we show that we can use distributional DP to solve them. We analyze distributional value and policy iteration, with bounds and a study of what objectives these distributional DP methods can or cannot optimize. We describe a number of applications outlining how to use distributional DP to solve different stock-augmented return distribution optimization problems, for example maximizing conditional value-at-risk, and homeostatic regulation. To highlight the practical potential of stock-augmented return distribution optimization and distributional DP, we combine the core ideas of distributional value iteration with the deep RL agent DQN, and empirically evaluate it for solving instances of the applications discussed.

Reinforcement learning is able to solve complex sequential decision-making tasks but is currently limited by sample efficiency and required computation. To improve sample efficiency, recent work focuses on model-based RL which interleaves model learning with planning. Recent methods further utilize policy learning, value estimation, and, self-supervised learning as auxiliary objectives. In this paper we show that, surprisingly, a simple representation learning approach relying only on a latent dynamics model trained by latent temporal consistency is sufficient for high-performance RL. This applies when using pure planning with a dynamics model conditioned on the representation, but, also when utilizing the representation as policy and value function features in model-free RL. In experiments, our approach learns an accurate dynamics model to solve challenging high-dimensional locomotion tasks with online planners while being 4.1 times faster to train compared to ensemble-based methods. With model-free RL without planning, especially on high-dimensional tasks, such as the DeepMind Control Suite Humanoid and Dog tasks, our approach outperforms model-free methods by a large margin and matches model-based methods' sample efficiency while training 2.4 times faster.

Reward specification plays a central role in reinforcement learning (RL), guiding the agent's behavior. To express non-Markovian rewards, formalisms such as reward machines have been introduced to capture dependencies on histories. However, traditional reward machines lack the ability to model precise timing constraints, limiting their use in time-sensitive applications. In this paper, we propose timed reward machines (TRMs), which are an extension of reward machines that incorporate timing constraints into the reward structure. TRMs enable more expressive specifications with tunable reward logic, for example, imposing costs for delays and granting rewards for timely actions. We study model-free RL frameworks (i.e., tabular Q-learning) for learning optimal policies with TRMs under digital and real-time semantics. Our algorithms integrate the TRM into learning via abstractions of timed automata, and employ counterfactual-imagining heuristics that exploit the structure of the TRM to improve the search. Experimentally, we demonstrate that our algorithm learns policies that achieve high rewards while satisfying the timing constraints specified by the TRM on popular RL benchmarks. Moreover, we conduct comparative studies of performance under different TRM semantics, along with ablations that highlight the benefits of counterfactual-imagining.

In this paper we argue for the fundamental importance of the value distribution: the distribution of the random return received by a reinforcement learning agent. This is in contrast to the common approach to reinforcement learning which models the expectation of this return, or value. Although there is an established body of literature studying the value distribution, thus far it has always been used for a specific purpose such as implementing risk-aware behaviour. We begin with theoretical results in both the policy evaluation and control settings, exposing a significant distributional instability in the latter. We then use the distributional perspective to design a new algorithm which applies Bellman's equation to the learning of approximate value distributions. We evaluate our algorithm using the suite of games from the Arcade Learning Environment. We obtain both state-of-the-art results and anecdotal evidence demonstrating the importance of the value distribution in approximate reinforcement learning. Finally, we combine theoretical and empirical evidence to highlight the ways in which the value distribution impacts learning in the approximate setting.

In this paper, we investigate the problem of offline Preference-based Reinforcement Learning (PbRL) with human feedback where feedback is available in the form of preference between trajectory pairs rather than explicit rewards. Our proposed algorithm consists of two main steps: (1) estimate the implicit reward using Maximum Likelihood Estimation (MLE) with general function approximation from offline data and (2) solve a distributionally robust planning problem over a confidence set around the MLE. We consider the general reward setting where the reward can be defined over the whole trajectory and provide a novel guarantee that allows us to learn any target policy with a polynomial number of samples, as long as the target policy is covered by the offline data. This guarantee is the first of its kind with general function approximation. To measure the coverage of the target policy, we introduce a new single-policy concentrability coefficient, which can be upper bounded by the per-trajectory concentrability coefficient. We also establish lower bounds that highlight the necessity of such concentrability and the difference from standard RL, where state-action-wise rewards are directly observed. We further extend and analyze our algorithm when the feedback is given over action pairs.

Reinforcement learning (RL) is a framework for solving sequential decision-making problems. In this work, we demonstrate that, surprisingly, RL emerges during the inference time of large language models (LLMs), a phenomenon we term in-context RL (ICRL). To reveal this capability, we introduce a simple multi-round prompting framework, we call ICRL prompting, for inference-time self-improvement. The goal of ICRL prompting is to guide LLMs to perform reinforcement learning during inference for self-improvement on a given task. After each response, the model receives numerical scalar feedback, denoted as a reward. In the next round, we prompt the LLM again together with a context that concatenates all prior responses and their associated rewards. We consistently observe that response quality improves as the context grows. In other words, the LLM can optimize scalar reward signals during inference, exhibiting behavior analogous to reinforcement learning. We evaluate ICRL prompting on Game of 24, creative writing, ScienceWorld, and Olympiad-level math competitions (AIME and HMMT), demonstrating significant improvements over baselines such as Self-Refine and Reflexion. Notably, even when the reward signals are generated by the same LLM, ICRL prompting still improves performance, highlighting a promising new paradigm for test-time scaling.

From out-competing grandmasters in chess to informing high-stakes healthcare decisions, emerging methods from artificial intelligence are increasingly capable of making complex and strategic decisions in diverse, high-dimensional, and uncertain situations. But can these methods help us devise robust strategies for managing environmental systems under great uncertainty? Here we explore how reinforcement learning, a subfield of artificial intelligence, approaches decision problems through a lens similar to adaptive environmental management: learning through experience to gradually improve decisions with updated knowledge. We review where reinforcement learning (RL) holds promise for improving evidence-informed adaptive management decisions even when classical optimization methods are intractable. For example, model-free deep RL might help identify quantitative decision strategies even when models are nonidentifiable. Finally, we discuss technical and social issues that arise when applying reinforcement learning to adaptive management problems in the environmental domain. Our synthesis suggests that environmental management and computer science can learn from one another about the practices, promises, and perils of experience-based decision-making.

The enduring challenge in the field of artificial intelligence has been the control of systems to achieve desired behaviours. While for systems governed by straightforward dynamics equations, methods like Linear Quadratic Regulation (LQR) have historically proven highly effective, most real-world tasks, which require a general problem-solver, demand world models with dynamics that cannot be easily described by simple equations. Consequently, these models must be learned from data using neural networks. Most model predictive control (MPC) algorithms designed for visual world models have traditionally explored gradient-free population-based optimisation methods, such as Cross Entropy and Model Predictive Path Integral (MPPI) for planning. However, we present an exploration of a gradient-based alternative that fully leverages the differentiability of the world model. In our study, we conduct a comparative analysis between our method and other MPC-based alternatives, as well as policy-based algorithms. In a sample-efficient setting, our method achieves on par or superior performance compared to the alternative approaches in most tasks. Additionally, we introduce a hybrid model that combines policy networks and gradient-based MPC, which outperforms pure policy based methods thereby holding promise for Gradient-based planning with world models in complex real-world tasks.

Offline reinforcement learning (RL) can in principle synthesize more optimal behavior from a dataset consisting only of suboptimal trials. One way that this can happen is by "stitching" together the best parts of otherwise suboptimal trajectories that overlap on similar states, to create new behaviors where each individual state is in-distribution, but the overall returns are higher. However, in many interesting and complex applications, such as autonomous navigation and dialogue systems, the state is partially observed. Even worse, the state representation is unknown or not easy to define. In such cases, policies and value functions are often conditioned on observation histories instead of states. In these cases, it is not clear if the same kind of "stitching" is feasible at the level of observation histories, since two different trajectories would always have different histories, and thus "similar states" that might lead to effective stitching cannot be leveraged. Theoretically, we show that standard offline RL algorithms conditioned on observation histories suffer from poor sample complexity, in accordance with the above intuition. We then identify sufficient conditions under which offline RL can still be efficient -- intuitively, it needs to learn a compact representation of history comprising only features relevant for action selection. We introduce a bisimulation loss that captures the extent to which this happens, and propose that offline RL can explicitly optimize this loss to aid worst-case sample complexity. Empirically, we show that across a variety of tasks either our proposed loss improves performance, or the value of this loss is already minimized as a consequence of standard offline RL, indicating that it correlates well with good performance.

We explore deep reinforcement learning methods for multi-agent domains. We begin by analyzing the difficulty of traditional algorithms in the multi-agent case: Q-learning is challenged by an inherent non-stationarity of the environment, while policy gradient suffers from a variance that increases as the number of agents grows. We then present an adaptation of actor-critic methods that considers action policies of other agents and is able to successfully learn policies that require complex multi-agent coordination. Additionally, we introduce a training regimen utilizing an ensemble of policies for each agent that leads to more robust multi-agent policies. We show the strength of our approach compared to existing methods in cooperative as well as competitive scenarios, where agent populations are able to discover various physical and informational coordination strategies.

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.