Daily Papers

Reinforcement learning algorithms are commonly analyzed (and designed) under the Markov assumption. This is unrealistic, as most environments encountered in practice are either partially observable, or require function approximation that restricts the agent to access non-Markovian state features. We consider the problem of learning an optimal reactive policy in a finite environment with deterministic observations (or equivalently, hard state aggregation). We introduce a new algorithm, Committed Q-learning, and prove almost-sure convergence to the optimal reactive policy under an intuitive assumption we call rewire-robustness. This assumption is strictly weaker than the q_star-realizability condition used in prior work. Our algorithm is a variant of classical Q-learning in which the behavior policy commits to a single action upon entering a feature, and only resamples actions when the observed feature changes. A crucial part of our analysis is the introduction of quasi-Markov environments.

Off-policy, value-based reinforcement learning methods such as Q-learning are appealing because they can learn from arbitrary experience, including data collected by older policies or other agents. In practice, however, bootstrapping makes long-horizon learning brittle: estimation errors at later states propagate backward through temporal-difference (TD) updates and can compound over time. We propose long-horizon Q-learning (LQL), which introduces a principled backstop against compounding error when learning the optimal action-value function. LQL builds on a prior optimality tightening observation: any realized action sequence lower-bounds what the optimal policy can achieve in expectation, so acting optimally earlier should not be worse than following the observed actions for several steps before switching to optimal behavior. Our contribution is to turn this inequality into a practical stabilization mechanism for Q-learning by using a hinge loss to penalize violations of these bounds. Importantly, LQL computes these penalties using network outputs already produced for the TD error, requiring no auxiliary networks and no additional forward passes relative to Q-learning. When combined with multiple state-of-the-art methods on a range of online and offline-to-online benchmarks, LQL consistently outperforms both 1-step TD and n-step TD learning at similar runtime.

Recently, supervised learning (SL) methodology has emerged as an effective approach for offline reinforcement learning (RL) due to their simplicity, stability, and efficiency. However, recent studies show that SL methods lack the trajectory stitching capability, typically associated with temporal difference (TD)-based approaches. A question naturally surfaces: How can we endow SL methods with stitching capability and bridge its performance gap with TD learning? To answer this question, we introduce Q-conditioned maximization supervised learning for offline goal-conditioned RL, which enhances SL with the stitching capability through Q-conditioned policy and Q-conditioned maximization. Concretely, we propose Goal-Conditioned Reinforced Supervised Learning (GCReinSL), which consists of (1) estimating the Q-function by CVAE from the offline dataset and (2) finding the maximum Q-value within the data support by integrating Q-function maximization with Expectile Regression. In inference time, our policy chooses optimal actions based on such a maximum Q-value. Experimental results from stitching evaluations on offline RL datasets demonstrate that our method outperforms prior SL approaches with stitching capabilities and goal data augmentation techniques.

In various real-world scenarios, interactions among agents often resemble the dynamics of general-sum games, where each agent strives to optimize its own utility. Despite the ubiquitous relevance of such settings, decentralized machine learning algorithms have struggled to find equilibria that maximize individual utility while preserving social welfare. In this paper we introduce Learning with Opponent Q-Learning Awareness (LOQA), a novel, decentralized reinforcement learning algorithm tailored to optimizing an agent's individual utility while fostering cooperation among adversaries in partially competitive environments. LOQA assumes the opponent samples actions proportionally to their action-value function Q. Experimental results demonstrate the effectiveness of LOQA at achieving state-of-the-art performance in benchmark scenarios such as the Iterated Prisoner's Dilemma and the Coin Game. LOQA achieves these outcomes with a significantly reduced computational footprint, making it a promising approach for practical multi-agent applications.

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

Deep Q-learning algorithms remain notoriously unstable, especially during early training when the maximization operator amplifies estimation errors. Inspired by bounded rationality theory and developmental learning, we introduce Sat-EnQ, a two-phase framework that first learns to be ``good enough'' before optimizing aggressively. In Phase 1, we train an ensemble of lightweight Q-networks under a satisficing objective that limits early value growth using a dynamic baseline, producing diverse, low-variance estimates while avoiding catastrophic overestimation. In Phase 2, the ensemble is distilled into a larger network and fine-tuned with standard Double DQN. We prove theoretically that satisficing induces bounded updates and cannot increase target variance, with a corollary quantifying conditions for substantial reduction. Empirically, Sat-EnQ achieves 3.8x variance reduction, eliminates catastrophic failures (0% vs 50% for DQN), maintains 79% performance under environmental noise}, and requires 2.5x less compute than bootstrapped ensembles. Our results highlight a principled path toward robust reinforcement learning by embracing satisficing before optimization.

Q-learning played a foundational role in the field reinforcement learning (RL). However, TD algorithms with off-policy data, such as Q-learning, or nonlinear function approximation like deep neural networks require several additional tricks to stabilise training, primarily a large replay buffer and target networks. Unfortunately, the delayed updating of frozen network parameters in the target network harms the sample efficiency and, similarly, the large replay buffer introduces memory and implementation overheads. In this paper, we investigate whether it is possible to accelerate and simplify off-policy TD training while maintaining its stability. Our key theoretical result demonstrates for the first time that regularisation techniques such as LayerNorm can yield provably convergent TD algorithms without the need for a target network or replay buffer, even with off-policy data. Empirically, we find that online, parallelised sampling enabled by vectorised environments stabilises training without the need for a large replay buffer. Motivated by these findings, we propose PQN, our simplified deep online Q-Learning algorithm. Surprisingly, this simple algorithm is competitive with more complex methods like: Rainbow in Atari, PPO-RNN in Craftax, QMix in Smax, and can be up to 50x faster than traditional DQN without sacrificing sample efficiency. In an era where PPO has become the go-to RL algorithm, PQN reestablishes off-policy Q-learning as a viable alternative.

Reinforcement Learning (RL) is an important machine learning paradigm for solving sequential decision-making problems. Recent years have witnessed remarkable progress in this field due to the rapid development of deep neural networks. However, the success of RL currently relies on extensive training data and computational resources. In addition, RL's limited ability to generalize across tasks restricts its applicability in dynamic and real-world environments. With the arisen of Continual Learning (CL), Continual Reinforcement Learning (CRL) has emerged as a promising research direction to address these limitations by enabling agents to learn continuously, adapt to new tasks, and retain previously acquired knowledge. In this survey, we provide a comprehensive examination of CRL, focusing on its core concepts, challenges, and methodologies. Firstly, we conduct a detailed review of existing works, organizing and analyzing their metrics, tasks, benchmarks, and scenario settings. Secondly, we propose a new taxonomy of CRL methods, categorizing them into four types from the perspective of knowledge storage and/or transfer. Finally, our analysis highlights the unique challenges of CRL and provides practical insights into future directions.

Given a set of trajectories demonstrating the execution of a task safely in a constrained MDP with observable rewards but with unknown constraints and non-observable costs, we aim to find a policy that maximizes the likelihood of demonstrated trajectories trading the balance between being conservative and increasing significantly the likelihood of high-rewarding trajectories but with potentially unsafe steps. Having these objectives, we aim towards learning a policy that maximizes the probability of the most promising trajectories with respect to the demonstrations. In so doing, we formulate the ``promise" of individual state-action pairs in terms of Q values, which depend on task-specific rewards as well as on the assessment of states' safety, mixing expectations in terms of rewards and safety. This entails a safe Q-learning perspective of the inverse learning problem under constraints: The devised Safe Q Inverse Constrained Reinforcement Learning (SafeQIL) algorithm is compared to state-of-the art inverse constraint reinforcement learning algorithms to a set of challenging benchmark tasks, showing its merits.

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.

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.

Long-horizon LLM agents can fail quietly: they settle on one reading of the evidence early, then spend the rest of the run defending it. We call this premature commitment. Final-answer scoring misses the failure mode because it sees only the answer, not whether the process has already collapsed to a stable path. We define representational commitment as cross-run hidden-state convergence at a fixed reasoning step, and use it as an early diagnostic of trajectory consistency. On Llama-3.1-70B running ReAct on HotpotQA, step-4 hidden-state similarity predicts downstream behavioral consistency (r = -0.35, partial r = -0.45), with a localized temporal and layer-wise signature. The signal replicates across Qwen-2.5-72B and Phi-3-14B, and on StrategyQA (r = -0.83). It does not track correctness: committed-wrong and committed-correct questions are not separable in activation similarity. That boundary is central to the claim. Commitment tells us whether an agent has settled, not whether it is right. A runtime monitor detects inconsistent trajectories from hidden states at AUROC up to 0.97 (0.85--0.88 under a stricter split), and a prompting intervention cuts behavioral variance by 28% against a token-matched control while leaving accuracy statistically unchanged. We also test whether the signal can route self-consistency compute; on a harder benchmark it helps only modestly and is matched by a simpler output-based baseline. The result is a diagnostic for a hidden process failure, with clear limits rather than a general accuracy lever.

Offline reinforcement learning faces a significant challenge of value over-estimation due to the distributional drift between the dataset and the current learned policy, leading to learning failure in practice. The common approach is to incorporate a penalty term to reward or value estimation in the Bellman iterations. Meanwhile, to avoid extrapolation on out-of-distribution (OOD) states and actions, existing methods focus on conservative Q-function estimation. In this paper, we propose Conservative State Value Estimation (CSVE), a new approach that learns conservative V-function via directly imposing penalty on OOD states. Compared to prior work, CSVE allows more effective in-data policy optimization with conservative value guarantees. Further, we apply CSVE and develop a practical actor-critic algorithm in which the critic does the conservative value estimation by additionally sampling and penalizing the states around the dataset, and the actor applies advantage weighted updates extended with state exploration to improve the policy. We evaluate in classic continual control tasks of D4RL, showing that our method performs better than the conservative Q-function learning methods and is strongly competitive among recent SOTA methods.

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.

In a standard view of the reinforcement learning problem, an agent's goal is to efficiently identify a policy that maximizes long-term reward. However, this perspective is based on a restricted view of learning as finding a solution, rather than treating learning as endless adaptation. In contrast, continual reinforcement learning refers to the setting in which the best agents never stop learning. Despite the importance of continual reinforcement learning, the community lacks a simple definition of the problem that highlights its commitments and makes its primary concepts precise and clear. To this end, this paper is dedicated to carefully defining the continual reinforcement learning problem. We formalize the notion of agents that "never stop learning" through a new mathematical language for analyzing and cataloging agents. Using this new language, we define a continual learning agent as one that can be understood as carrying out an implicit search process indefinitely, and continual reinforcement learning as the setting in which the best agents are all continual learning agents. We provide two motivating examples, illustrating that traditional views of multi-task reinforcement learning and continual supervised learning are special cases of our definition. Collectively, these definitions and perspectives formalize many intuitive concepts at the heart of learning, and open new research pathways surrounding continual learning agents.

Reinforcement learning is time-consuming for complex tasks due to the need for large amounts of training data. Recent advances in GPU-based simulation, such as Isaac Gym, have sped up data collection thousands of times on a commodity GPU. Most prior works used on-policy methods like PPO due to their simplicity and ease of scaling. Off-policy methods are more data efficient but challenging to scale, resulting in a longer wall-clock training time. This paper presents a Parallel Q-Learning (PQL) scheme that outperforms PPO in wall-clock time while maintaining superior sample efficiency of off-policy learning. PQL achieves this by parallelizing data collection, policy learning, and value learning. Different from prior works on distributed off-policy learning, such as Apex, our scheme is designed specifically for massively parallel GPU-based simulation and optimized to work on a single workstation. In experiments, we demonstrate that Q-learning can be scaled to tens of thousands of parallel environments and investigate important factors affecting learning speed. The code is available at https://github.com/Improbable-AI/pql.

Offline reinforcement learning learns an effective policy on offline datasets without online interaction, and it attracts persistent research attention due to its potential of practical application. However, extrapolation error generated by distribution shift will still lead to the overestimation for those actions that transit to out-of-distribution(OOD) states, which degrades the reliability and robustness of the offline policy. In this paper, we propose Contextual Conservative Q-Learning(C-CQL) to learn a robustly reliable policy through the contextual information captured via an inverse dynamics model. With the supervision of the inverse dynamics model, it tends to learn a policy that generates stable transition at perturbed states, for the fact that pertuebed states are a common kind of OOD states. In this manner, we enable the learnt policy more likely to generate transition that destines to the empirical next state distributions of the offline dataset, i.e., robustly reliable transition. Besides, we theoretically reveal that C-CQL is the generalization of the Conservative Q-Learning(CQL) and aggressive State Deviation Correction(SDC). Finally, experimental results demonstrate the proposed C-CQL achieves the state-of-the-art performance in most environments of offline Mujoco suite and a noisy Mujoco setting.

We study model-free Q-learning in finite-horizon episodic Markov Decision Processes (MDPs) with stationary dynamics across episodes. We identify a central issue in nascent model-free posterior-sampling works: the reliance on delayed learning in order to prove theoretical guarantees. In particular, we identify three opportunities for faster learning - (i) value-function update order, (ii) update frequencies, and (iii) value-function initialization. Using Wang et al.'s RandomizedQ as a basis, we illustrate these changes and their individual (as well as cumulative) impact in multiple empirical studies. We find that our combined modifications, termed ReversedQ, improve scaled mean cumulative reward compared to RandomizedQ, from 9.53% to 78.78% in the Bidirectional Diabolical Combination Lock (BDCL), and from 21.76% to 61.81% in a chain MDP.

Expressive continuous control policies, such as diffusion and flow models, form the backbone of recent advances in scaling imitation learning for simulated and real robot control. While they are known to scale stably in the supervised imitation learning setting, incorporating them into reinforcement learning (RL) pipelines for policy improvement has proven more difficult. It often requires specialized training objectives or backpropagating through denoising processes, which cause well-known issues with stability and affect scalability. In this paper we study the question of whether simple policy improvement schemes at test time alone, leaving stable supervised policy training intact, can be a competitive alternative which sidesteps these issues. To this end, we propose QGF (Q-Guided Flow), an RL algorithm that performs policy optimization entirely at test time. QGF works by pre-training both a reference flow policy (via a standard behavioral cloning objective) and a value function critic and, at test time, using the value gradient to guide the reference policy to generate higher-value actions without any additional policy learning. Empirically, QGF outperforms prior test-time RL methods on single-task and goal-conditioned offline RL benchmarks with high-dimensional action spaces, and is competitive with state-of-the-art training-time algorithms while being much cheaper to run. Moreover, it exhibits favorable scaling with model size by avoiding the instability of actor-critic training, offering a practical and effective alternative RL algorithm with expressive policies.

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.

Despite the great empirical success of deep reinforcement learning, its theoretical foundation is less well understood. In this work, we make the first attempt to theoretically understand the deep Q-network (DQN) algorithm (Mnih et al., 2015) from both algorithmic and statistical perspectives. In specific, we focus on a slight simplification of DQN that fully captures its key features. Under mild assumptions, we establish the algorithmic and statistical rates of convergence for the action-value functions of the iterative policy sequence obtained by DQN. In particular, the statistical error characterizes the bias and variance that arise from approximating the action-value function using deep neural network, while the algorithmic error converges to zero at a geometric rate. As a byproduct, our analysis provides justifications for the techniques of experience replay and target network, which are crucial to the empirical success of DQN. Furthermore, as a simple extension of DQN, we propose the Minimax-DQN algorithm for zero-sum Markov game with two players. Borrowing the analysis of DQN, we also quantify the difference between the policies obtained by Minimax-DQN and the Nash equilibrium of the Markov game in terms of both the algorithmic and statistical rates of convergence.

The fine-tuning of pre-trained large language models (LLMs) using reinforcement learning (RL) is generally formulated as direct policy optimization. This approach was naturally favored as it efficiently improves a pretrained LLM, seen as an initial policy. Another RL paradigm, Q-learning methods, has received far less attention in the LLM community while demonstrating major success in various non-LLM RL tasks. In particular, Q-learning effectiveness comes from its sample efficiency and ability to learn offline, which is particularly valuable given the high computational cost of sampling with LLMs. However, naively applying a Q-learning-style update to the model's logits is ineffective due to the specificity of LLMs. Our core contribution is to derive theoretically grounded loss functions from Bellman equations to adapt Q-learning methods to LLMs. To do so, we carefully adapt insights from the RL literature to account for LLM-specific characteristics, ensuring that the logits become reliable Q-value estimates. We then use this loss to build a practical algorithm, ShiQ for Shifted-Q, that supports off-policy, token-wise learning while remaining simple to implement. Finally, we evaluate ShiQ on both synthetic data and real-world benchmarks, e.g., UltraFeedback and BFCL-V3, demonstrating its effectiveness in both single-turn and multi-turn LLM settings

Multi-agent reinforcement learning in dynamic social dilemmas commonly relies on parameter sharing to enable scalability. We show that in shared-policy Deep Q-Network learning, standard exploration can induce a robust and systematic collapse of cooperation even in environments where fully cooperative equilibria are stable and payoff dominant. Through controlled experiments, we demonstrate that shared DQN converges to stable but persistently low-cooperation regimes. This collapse is not caused by reward misalignment, noise, or insufficient training, but by a representational failure arising from partial observability combined with parameter coupling across heterogeneous agent states. Exploration-driven updates bias the shared representation toward locally dominant defection responses, which then propagate across agents and suppress cooperative learning. We confirm that the failure persists across network sizes, exploration schedules, and payoff structures, and disappears when parameter sharing is removed or when agents maintain independent representations. These results identify a fundamental failure mode of shared-policy MARL and establish structural conditions under which scalable learning architectures can systematically undermine cooperation. Our findings provide concrete guidance for the design of multi-agent learning systems in social and economic environments where collective behavior is critical.

A commonly used heuristic in RL is experience replay (e.g.~lin1993reinforcement, mnih2015human), in which a learner stores and re-uses past trajectories as if they were sampled online. In this work, we initiate a rigorous study of this heuristic in the setting of tabular Q-learning. We provide a convergence rate guarantee, and discuss how it compares to the convergence of Q-learning depending on important parameters such as the frequency and number of replay iterations. We also provide theoretical evidence showing when we might expect this heuristic to strictly improve performance, by introducing and analyzing a simple class of MDPs. Finally, we provide some experiments to support our theoretical findings.

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

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.

Reinforcement learning (RL) has improved the reasoning abilities of large language models (LLMs), yet state-of-the-art methods still fail to learn on many training problems. On hard problems, on-policy RL rarely explores even a single correct rollout, yielding zero reward and no learning signal for driving improvement. We find that natural solutions to remedy this exploration problem from classical RL, such as entropy bonuses, more permissive clipping of the importance ratio, or direct optimization of pass@k objectives, do not resolve this issue and often destabilize optimization without improving solvability. A natural alternative is to leverage transfer from easier problems. However, we show that mixing easy and hard problems during RL training is counterproductive due to ray interference, where optimization focuses on already-solvable problems in a way that actively inhibits progress on harder ones. To address this challenge, we introduce Privileged On-Policy Exploration (POPE), an approach that leverages human- or other oracle solutions as privileged information to guide exploration on hard problems, unlike methods that use oracle solutions as training targets (e.g., off-policy RL methods or warmstarting from SFT). POPE augments hard problems with prefixes of oracle solutions, enabling RL to obtain non-zero rewards during guided rollouts. Crucially, the resulting behaviors transfer back to the original, unguided problems through a synergy between instruction-following and reasoning. Empirically, POPE expands the set of solvable problems and substantially improves performance on challenging reasoning benchmarks.

This research focuses on enhancing reinforcement learning (RL) algorithms by integrating penalty functions to guide agents in avoiding unwanted actions while optimizing rewards. The goal is to improve the learning process by ensuring that agents learn not only suitable actions but also which actions to avoid. Additionally, we reintroduce a bidirectional learning approach that enables agents to learn from both initial and terminal states, thereby improving speed and robustness in complex environments. Our proposed Penalty-Based Bidirectional methodology is tested against Mani skill benchmark environments, demonstrating an optimality improvement of success rate of approximately 4% compared to existing RL implementations. The findings indicate that this integrated strategy enhances policy learning, adaptability, and overall performance in challenging scenarios

Offline reinforcement learning requires reconciling two conflicting aims: learning a policy that improves over the behavior policy that collected the dataset, while at the same time minimizing the deviation from the behavior policy so as to avoid errors due to distributional shift. This trade-off is critical, because most current offline reinforcement learning methods need to query the value of unseen actions during training to improve the policy, and therefore need to either constrain these actions to be in-distribution, or else regularize their values. We propose an offline RL method that never needs to evaluate actions outside of the dataset, but still enables the learned policy to improve substantially over the best behavior in the data through generalization. The main insight in our work is that, instead of evaluating unseen actions from the latest policy, we can approximate the policy improvement step implicitly by treating the state value function as a random variable, with randomness determined by the action (while still integrating over the dynamics to avoid excessive optimism), and then taking a state conditional upper expectile of this random variable to estimate the value of the best actions in that state. This leverages the generalization capacity of the function approximator to estimate the value of the best available action at a given state without ever directly querying a Q-function with this unseen action. Our algorithm alternates between fitting this upper expectile value function and backing it up into a Q-function. Then, we extract the policy via advantage-weighted behavioral cloning. We dub our method implicit Q-learning (IQL). IQL demonstrates the state-of-the-art performance on D4RL, a standard benchmark for offline reinforcement learning. We also demonstrate that IQL achieves strong performance fine-tuning using online interaction after offline initialization.

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.

We propose Q-learning with Adjoint Matching (QAM), a novel TD-based reinforcement learning (RL) algorithm that tackles a long-standing challenge in continuous-action RL: efficient optimization of an expressive diffusion or flow-matching policy with respect to a parameterized Q-function. Effective optimization requires exploiting the first-order information of the critic, but it is challenging to do so for flow or diffusion policies because direct gradient-based optimization via backpropagation through their multi-step denoising process is numerically unstable. Existing methods work around this either by only using the value and discarding the gradient information, or by relying on approximations that sacrifice policy expressivity or bias the learned policy. QAM sidesteps both of these challenges by leveraging adjoint matching, a recently proposed technique in generative modeling, which transforms the critic's action gradient to form a step-wise objective function that is free from unstable backpropagation, while providing an unbiased, expressive policy at the optimum. Combined with temporal-difference backup for critic learning, QAM consistently outperforms prior approaches on hard, sparse reward tasks in both offline and offline-to-online RL.

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.

When applying offline reinforcement learning (RL) in healthcare scenarios, the out-of-distribution (OOD) issues pose significant risks, as inappropriate generalization beyond clinical expertise can result in potentially harmful recommendations. While existing methods like conservative Q-learning (CQL) attempt to address the OOD issue, their effectiveness is limited by only constraining action selection by suppressing uncertain actions. This action-only regularization imitates clinician actions that prioritize short-term rewards, but it fails to regulate downstream state trajectories, thereby limiting the discovery of improved long-term treatment strategies. To safely improve policy beyond clinician recommendations while ensuring that state-action trajectories remain in-distribution, we propose Offline Guarded Safe Reinforcement Learning (OGSRL), a theoretically grounded model-based offline RL framework. OGSRL introduces a novel dual constraint mechanism for improving policy with reliability and safety. First, the OOD guardian is established to specify clinically validated regions for safe policy exploration. By constraining optimization within these regions, it enables the reliable exploration of treatment strategies that outperform clinician behavior by leveraging the full patient state history, without drifting into unsupported state-action trajectories. Second, we introduce a safety cost constraint that encodes medical knowledge about physiological safety boundaries, providing domain-specific safeguards even in areas where training data might contain potentially unsafe interventions. Notably, we provide theoretical guarantees on safety and near-optimality: policies that satisfy these constraints remain in safe and reliable regions and achieve performance close to the best possible policy supported by the data.

We study the problem of designing mechanisms for information acquisition scenarios. This setting models strategic interactions between an uniformed receiver and a set of informed senders. In our model the senders receive information about the underlying state of nature and communicate their observation (either truthfully or not) to the receiver, which, based on this information, selects an action. Our goal is to design mechanisms maximizing the receiver's utility while incentivizing the senders to report truthfully their information. First, we provide an algorithm that efficiently computes an optimal incentive compatible (IC) mechanism. Then, we focus on the online problem in which the receiver sequentially interacts in an unknown game, with the objective of minimizing the cumulative regret w.r.t. the optimal IC mechanism, and the cumulative violation of the incentive compatibility constraints. We investigate two different online scenarios, i.e., the full and bandit feedback settings. For the full feedback problem, we propose an algorithm that guarantees mathcal O(sqrt T) regret and violation, while for the bandit feedback setting we present an algorithm that attains mathcal O(T^{alpha}) regret and mathcal O(T^{1-alpha/2}) violation for any alphain[1/2, 1]. Finally, we complement our results providing a tight lower bound.

Learning in environments with large state and action spaces, and sparse rewards, can hinder a Reinforcement Learning (RL) agent's learning through trial-and-error. For instance, following natural language instructions on the Web (such as booking a flight ticket) leads to RL settings where input vocabulary and number of actionable elements on a page can grow very large. Even though recent approaches improve the success rate on relatively simple environments with the help of human demonstrations to guide the exploration, they still fail in environments where the set of possible instructions can reach millions. We approach the aforementioned problems from a different perspective and propose guided RL approaches that can generate unbounded amount of experience for an agent to learn from. Instead of learning from a complicated instruction with a large vocabulary, we decompose it into multiple sub-instructions and schedule a curriculum in which an agent is tasked with a gradually increasing subset of these relatively easier sub-instructions. In addition, when the expert demonstrations are not available, we propose a novel meta-learning framework that generates new instruction following tasks and trains the agent more effectively. We train DQN, deep reinforcement learning agent, with Q-value function approximated with a novel QWeb neural network architecture on these smaller, synthetic instructions. We evaluate the ability of our agent to generalize to new instructions on World of Bits benchmark, on forms with up to 100 elements, supporting 14 million possible instructions. The QWeb agent outperforms the baseline without using any human demonstration achieving 100% success rate on several difficult environments.

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.

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.

Reinforcement Learning from Human Feedback (RLHF) has proven effective in aligning large language models with human intentions, yet it often relies on complex methodologies like Proximal Policy Optimization (PPO) that require extensive hyper-parameter tuning and present challenges in sample efficiency and stability. In this paper, we introduce Inverse-Q*, an innovative framework that transcends traditional RL methods by optimizing token-level reinforcement learning without the need for additional reward or value models. Inverse-Q* leverages direct preference optimization techniques but extends them by estimating the conditionally optimal policy directly from the model's responses, facilitating more granular and flexible policy shaping. Our approach reduces reliance on human annotation and external supervision, making it especially suitable for low-resource settings. We present extensive experimental results demonstrating that Inverse-Q* not only matches but potentially exceeds the effectiveness of PPO in terms of convergence speed and the alignment of model responses with human preferences. Our findings suggest that Inverse-Q* offers a practical and robust alternative to conventional RLHF approaches, paving the way for more efficient and adaptable model training approaches.

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.

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

In recent years, Reinforcement Learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maximizing the reward, rarely accomplishing both objectives simultaneously. Here, we address this problem by introducing Reinforcement Learning with Optimistic Ascent-Descent (ReLOAD), a principled CRL method with guaranteed last-iterate convergence. We demonstrate its empirical effectiveness on a wide variety of CRL problems including discrete MDPs and continuous control. In the process we establish a benchmark of challenging CRL problems.

Recent advancements in reasoning-focused language models such as OpenAI's O1 and DeepSeek-R1 have shown that scaling test-time computation-through chain-of-thought reasoning and iterative exploration-can yield substantial improvements on complex tasks like mathematics and code generation. These breakthroughs have been driven by large-scale reinforcement learning (RL), particularly when combined with verifiable reward signals that provide objective and grounded supervision. In this report, we investigate the effects of prolonged reinforcement learning on a small language model across a diverse set of reasoning domains. Our work identifies several key ingredients for effective training, including the use of verifiable reward tasks, enhancements to Group Relative Policy Optimization (GRPO), and practical techniques to improve training stability and generalization. We introduce controlled KL regularization, clipping ratio, and periodic reference policy resets as critical components for unlocking long-term performance gains. Our model achieves significant improvements over strong baselines, including +14.7% on math, +13.9% on coding, and +54.8% on logic puzzle tasks. To facilitate continued research, we release our model publicly.

Modern reinforcement learning (RL) systems capture deep truths about general, human problem-solving. In domains where new data can be simulated cheaply, these systems uncover sequential decision-making policies that far exceed the ability of any human. Society faces many problems whose solutions require this skill, but they are often in domains where new data cannot be cheaply simulated. In such scenarios, we can learn simulators from existing data, but these will only ever be approximately correct, and can be pathologically incorrect when queried outside of their training distribution. As a result, a misalignment between the environments in which we train our agents and the real-world in which we wish to deploy our agents is inevitable. Dealing with this misalignment is the primary concern of zero-shot reinforcement learning, a problem setting where the agent must generalise to a new task or domain with zero practice shots. Whilst impressive progress has been made on methods that perform zero-shot RL in idealised settings, new work is needed if these results are to be replicated in real-world settings. In this thesis, we argue that doing so requires us to navigate (at least) three constraints. First, the data quality constraint: real-world datasets are small and homogeneous. Second, the observability constraint: states, dynamics and rewards in the real-world are often only partially observed. And third, the data availability constraint: a priori access to data cannot always be assumed. This work proposes a suite of methods that perform zero-shot RL subject to these constraints. In a series of empirical studies we expose the failings of existing methods, and justify our techniques for remedying them. We believe these designs take us a step closer to RL methods that can be deployed to solve real-world problems.

Iterative generative modeling techniques, such as flow matching, provide powerful tools to model complex behaviors for effective offline reinforcement learning (RL). In this work, we propose a new off-policy RL algorithm that trains a flow policy based on prior data. Our idea starts from the "expanded" Markov decision process (MDP) framework, which treats individual flow refinement steps as separate actions in an MDP. To enable off-policy RL within this framework, we apply two techniques: we generate virtual on-policy trajectories (by "reversing" flows) to make this framework compatible with prior data, and we apply a bias-and-variance reduction technique to mitigate the curse of horizon in off-policy RL. We call the resulting algorithm Reversal Q-learning (RQL). RQL has several advantages over previous flow-based RL methods: it does not suffer from backpropagation through time, makes better use of the learned value function, and directly trains the full, expressive flow policy. Through our experiments on 50 challenging simulated robotic tasks, we show that RQL leads to the best average offline RL performance compared to state-of-the-art flow-based offline RL algorithms.

Recent reinforcement learning (RL) methods have substantially enhanced the planning capabilities of Large Language Models (LLMs), yet the theoretical basis for their effectiveness remains elusive. In this work, we investigate RL's benefits and limitations through a tractable graph-based abstraction, focusing on policy gradient (PG) and Q-learning methods. Our theoretical analyses reveal that supervised fine-tuning (SFT) may introduce co-occurrence-based spurious solutions, whereas RL achieves correct planning primarily through exploration, underscoring exploration's role in enabling better generalization. However, we also show that PG suffers from diversity collapse, where output diversity decreases during training and persists even after perfect accuracy is attained. By contrast, Q-learning provides two key advantages: off-policy learning and diversity preservation at convergence. We further demonstrate that careful reward design is necessary to prevent reward hacking in Q-learning. Finally, applying our framework to the real-world planning benchmark Blocksworld, we confirm that these behaviors manifest in practice.

We present an approach called Q-probing to adapt a pre-trained language model to maximize a task-specific reward function. At a high level, Q-probing sits between heavier approaches such as finetuning and lighter approaches such as few shot prompting, but can also be combined with either. The idea is to learn a simple linear function on a model's embedding space that can be used to reweight candidate completions. We theoretically show that this sampling procedure is equivalent to a KL-constrained maximization of the Q-probe as the number of samples increases. To train the Q-probes we consider either reward modeling or a class of novel direct policy learning objectives based on importance weighted policy gradients. With this technique, we see gains in domains with ground-truth rewards (code generation) as well as implicit rewards defined by preference data, even outperforming finetuning in data-limited regimes. Moreover, a Q-probe can be trained on top of an API since it only assumes access to sampling and embeddings. Code: https://github.com/likenneth/q_probe .

When safety is formulated as a limit of cumulative cost, safe reinforcement learning (RL) aims to learn policies that maximize return subject to the cost constraint in data collection and deployment. Off-policy safe RL methods, although offering high sample efficiency, suffer from constraint violations due to cost-agnostic exploration and estimation bias in cumulative cost. To address this issue, we propose Constrained Optimistic eXploration Q-learning (COX-Q), an off-policy safe RL algorithm that integrates cost-bounded online exploration and conservative offline distributional value learning. First, we introduce a novel cost-constrained optimistic exploration strategy that resolves gradient conflicts between reward and cost in the action space and adaptively adjusts the trust region to control the training cost. Second, we adopt truncated quantile critics to stabilize the cost value learning. Quantile critics also quantify epistemic uncertainty to guide exploration. Experiments on safe velocity, safe navigation, and autonomous driving tasks demonstrate that COX-Q achieves high sample efficiency, competitive test safety performance, and controlled data collection cost. The results highlight COX-Q as a promising RL method for safety-critical applications.

Reinforcement learning (RL) tasks are typically framed as Markov Decision Processes (MDPs), assuming that decisions are made at fixed time intervals. However, many applications of great importance, including healthcare, do not satisfy this assumption, yet they are commonly modelled as MDPs after an artificial reshaping of the data. In addition, most healthcare (and similar) problems are offline by nature, allowing for only retrospective studies. To address both challenges, we begin by discussing the Semi-MDP (SMDP) framework, which formally handles actions of variable timings. We next present a formal way to apply SMDP modifications to nearly any given value-based offline RL method. We use this theory to introduce three SMDP-based offline RL algorithms, namely, SDQN, SDDQN, and SBCQ. We then experimentally demonstrate that only these SMDP-based algorithms learn the optimal policy in variable-time environments, whereas their MDP counterparts do not. Finally, we apply our new algorithms to a real-world offline dataset pertaining to warfarin dosing for stroke prevention and demonstrate similar results.

We develop a Multi-Agent Reinforcement Learning (MARL) method to learn scalable control policies for target tracking. Our method can handle an arbitrary number of pursuers and targets; we show results for tasks consisting up to 1000 pursuers tracking 1000 targets. We use a decentralized, partially-observable Markov Decision Process framework to model pursuers as agents receiving partial observations (range and bearing) about targets which move using fixed, unknown policies. An attention mechanism is used to parameterize the value function of the agents; this mechanism allows us to handle an arbitrary number of targets. Entropy-regularized off-policy RL methods are used to train a stochastic policy, and we discuss how it enables a hedging behavior between pursuers that leads to a weak form of cooperation in spite of completely decentralized control execution. We further develop a masking heuristic that allows training on smaller problems with few pursuers-targets and execution on much larger problems. Thorough simulation experiments, ablation studies, and comparisons to state of the art algorithms are performed to study the scalability of the approach and robustness of performance to varying numbers of agents and targets.

As it becomes increasingly difficult to monolithically scale a quantum processor, distributed quantum computing (DQC) offers an alternative by distributing qubits across multiple smaller interconnected quantum processor modules. In such an architecture, the challenge of quantum circuit compilation shifts from placing and routing qubits within one module to placing, routing and using the qubits efficiently across modules. In order to optimize circuit execution time, the right state-dependent networking decisions must be found, such as when and where to generate shared remote quantum states to support remote operations. Reinforcement learning (RL) provides a natural framework for this problem, generating a compilation policy that can generalize across different circuits. Building on the framework of Promponas et al. (2024), we introduce an agent that combines a novel action-space formulation with effective action-masking strategies. A comprehensive numerical comparison of the two approaches under different coupling constraints shows that our agent achieves improved training and inference performance with a relative reduction in the modeled execution time of up to 35\%.

There is growing interest in utilizing flow-based models as decision-making policies in reinforcement learning due to their high expressive capacity. However, effectively leveraging this expressivity for value maximization remains challenging, as naive gradient-based optimization requires backpropagating through numerical solvers and often leads to instability. Existing approaches typically address this issue by restricting the expressive capacity of flow-based policies, resulting in a trade-off between optimization stability and representational flexibility. To resolve this, we introduce Q-Flow, a framework that leverages the deterministic nature of flow dynamics to explicitly propagate terminal trajectory value to intermediate latent states along the policy-induced flow. This formulation enables stable policy optimization using intermediate value gradients without unrolling the numerical solver, effectively bridging the gap between stability and expressivity. We evaluate Q-Flow in the offline learning setting on the challenging OGBench suite, where it consistently outperforms state-of-the-art baselines by an average of 10.6 percentage points, while also enabling stable online adaptation within the same framework.

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

RL with Verifiable Rewards (RLVR) has emerged as a promising paradigm for improving the reasoning abilities of large language models (LLMs). Current methods rely primarily on policy optimization frameworks like PPO and GRPO, which follow generalized policy iteration that alternates between evaluating the current policy's value and improving the policy based on evaluation. While effective, they often suffer from training instability and diversity collapse, requiring complex heuristic tricks and careful tuning. We observe that standard RLVR in math reasoning can be formalized as a specialized finite-horizon Markov Decision Process with deterministic state transitions, tree-structured dynamics, and binary terminal rewards. Though large in scale, the underlying structure is simpler than general-purpose control settings for which popular RL algorithms (e.g., PPO) were developed, suggesting that several sophisticated techniques in existing methods may be reduced or even omitted. Based on this insight, we prove a surprising result: the optimal action can be recovered from the Q-function of a fixed uniformly random policy, thereby bypassing the generalized policy iteration loop and its associated heuristics. We introduce Random Policy Valuation for Diverse Reasoning (ROVER) to translate this principle into a practical and scalable algorithm for LLM math reasoning, a minimalist yet highly effective RL method that samples actions from a softmax over these uniform-policy Q-values. ROVER preserves diversity throughout training, allowing sustained exploration of multiple valid pathways. Across multiple base models and standard math reasoning benchmarks, ROVER demonstrates superior performance in both quality (+8.2 on pass@1, +16.8 on pass@256) and diversity (+17.6\%), despite its radical simplification compared to strong, complicated existing methods.

Emergent cooperation in classical Multi-Agent Reinforcement Learning has gained significant attention, particularly in the context of Sequential Social Dilemmas (SSDs). While classical reinforcement learning approaches have demonstrated capability for emergent cooperation, research on extending these methods to Quantum Multi-Agent Reinforcement Learning remains limited, particularly through communication. In this paper, we apply communication approaches to quantum Q-Learning agents: the Mutual Acknowledgment Token Exchange (MATE) protocol, its extension Mutually Endorsed Distributed Incentive Acknowledgment Token Exchange (MEDIATE), the peer rewarding mechanism Gifting, and Reinforced Inter-Agent Learning (RIAL). We evaluate these approaches in three SSDs: the Iterated Prisoner's Dilemma, Iterated Stag Hunt, and Iterated Game of Chicken. Our experimental results show that approaches using MATE with temporal-difference measure (MATETD), AutoMATE, MEDIATE-I, and MEDIATE-S achieved high cooperation levels across all dilemmas, demonstrating that communication is a viable mechanism for fostering emergent cooperation in Quantum Multi-Agent Reinforcement Learning.

In this paper, we introduce Randomized Q-learning (RandQL), a novel randomized model-free algorithm for regret minimization in episodic Markov Decision Processes (MDPs). To the best of our knowledge, RandQL is the first tractable model-free posterior sampling-based algorithm. We analyze the performance of RandQL in both tabular and non-tabular metric space settings. In tabular MDPs, RandQL achieves a regret bound of order O(H^{5SAT}), where H is the planning horizon, S is the number of states, A is the number of actions, and T is the number of episodes. For a metric state-action space, RandQL enjoys a regret bound of order O(H^{5/2} T^{(d_z+1)/(d_z+2)}), where d_z denotes the zooming dimension. Notably, RandQL achieves optimistic exploration without using bonuses, relying instead on a novel idea of learning rate randomization. Our empirical study shows that RandQL outperforms existing approaches on baseline exploration environments.

We study the adaption of Soft Actor-Critic (SAC), which is considered as a state-of-the-art reinforcement learning (RL) algorithm, from continuous action space to discrete action space. We revisit vanilla discrete SAC and provide an in-depth understanding of its Q value underestimation and performance instability issues when applied to discrete settings. We thereby propose Stable Discrete SAC (SDSAC), an algorithm that leverages entropy-penalty and double average Q-learning with Q-clip to address these issues. Extensive experiments on typical benchmarks with discrete action space, including Atari games and a large-scale MOBA game, show the efficacy of our proposed method. Our code is at: https://github.com/coldsummerday/SD-SAC.git.

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

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.

In Reinforcement Learning (RL), regularization has emerged as a popular tool both in theory and practice, typically based either on an entropy bonus or a Kullback-Leibler divergence that constrains successive policies. In practice, these approaches have been shown to improve exploration, robustness and stability, giving rise to popular Deep RL algorithms such as SAC and TRPO. Policy Mirror Descent (PMD) is a theoretical framework that solves this general regularized policy optimization problem, however the closed-form solution involves the sum of all past Q-functions, which is intractable in practice. We propose and analyze PMD-like algorithms that only keep the last M Q-functions in memory, and show that for finite and large enough M, a convergent algorithm can be derived, introducing no error in the policy update, unlike prior deep RL PMD implementations. StaQ, the resulting algorithm, enjoys strong theoretical guarantees and is competitive with deep RL baselines, while exhibiting less performance oscillation, paving the way for fully stable deep RL algorithms and providing a testbed for experimentation with Policy Mirror Descent.

We adapt the ideas underlying the success of Deep Q-Learning to the continuous action domain. We present an actor-critic, model-free algorithm based on the deterministic policy gradient that can operate over continuous action spaces. Using the same learning algorithm, network architecture and hyper-parameters, our algorithm robustly solves more than 20 simulated physics tasks, including classic problems such as cartpole swing-up, dexterous manipulation, legged locomotion and car driving. Our algorithm is able to find policies whose performance is competitive with those found by a planning algorithm with full access to the dynamics of the domain and its derivatives. We further demonstrate that for many of the tasks the algorithm can learn policies end-to-end: directly from raw pixel inputs.

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.

Reinforcement learning (RL) promises to expand the capabilities of language models, but it is unclear if current RL techniques promote the discovery of novel behaviors, or simply sharpen those already present in the base model. In this paper, we investigate the value of deliberate exploration -- explicitly incentivizing the model to discover novel and diverse behaviors -- and aim to understand how the knowledge in pre-trained models can guide this search. Our main finding is that exploration with a simple, principled, representation-based bonus derived from the pre-trained language model's hidden states significantly improves diversity and pass@k rates -- both for post-training, and in a novel inference-time scaling setting we introduce. For inference-time, exploration with representation-based diversity improves efficiency, consistently improving pass@k rates across a variety of models and reasoning tasks. For example, for Qwen-2.5-14b-Instruct we obtain over 50% improvement in verifier efficiency on almost all tasks. For post-training, we show that integrating this exploration strategy into an RL pipeline improves reasoning performance over that of the initial model and over standard RL post-training. For example, on AIME 2024, our post-trained Qwen-2.5-7b-Instruct's pass@80 matches the pass@256 of GRPO on the same model, demonstrating a 3x improvement in test-time sample efficiency. Overall, our findings suggest that deliberate exploration -- with the right notion of diversity -- is a practical path toward discovery of new behaviors beyond sharpening.

Offline multi-agent reinforcement learning is challenging due to the coupling effect of both distribution shift issue common in offline setting and the high dimension issue common in multi-agent setting, making the action out-of-distribution (OOD) and value overestimation phenomenon excessively severe. Tomitigate this problem, we propose a novel multi-agent offline RL algorithm, named CounterFactual Conservative Q-Learning (CFCQL) to conduct conservative value estimation. Rather than regarding all the agents as a high dimensional single one and directly applying single agent methods to it, CFCQL calculates conservative regularization for each agent separately in a counterfactual way and then linearly combines them to realize an overall conservative value estimation. We prove that it still enjoys the underestimation property and the performance guarantee as those single agent conservative methods do, but the induced regularization and safe policy improvement bound are independent of the agent number, which is therefore theoretically superior to the direct treatment referred to above, especially when the agent number is large. We further conduct experiments on four environments including both discrete and continuous action settings on both existing and our man-made datasets, demonstrating that CFCQL outperforms existing methods on most datasets and even with a remarkable margin on some of them.

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.

LLM agents increasingly act over long horizons, where a single trajectory can contain hundreds or thousands of actions. In these settings, outcome-only rewards provide too sparse guidance, failing to inform the model about the goodness of intermediate actions. Dense supervision methods aim to solve this problem by scoring intermediate steps, from intrinsic confidence to self-distillation and embedding similarities. However, it is common practice to evaluate them by measuring the downstream performance of a training pipeline that integrates them. This is expensive, conflates supervision quality with training engineering confounders, and renders different methodological families requiring distinct training setups incomparable. As a result, dense supervision methods are rarely benchmarked on common ground. We introduce QVal, a training-free testbed for directly evaluating dense supervision signals. Given a state-action pair, QVal measures how well a method's score is Q-aligned: whether it orders actions according to the Q-values of a strong reference-policy. This lets us compare signals before any training run and separate signal quality from other engineering choices. We instantiate QVal as QVal-v1.0, benchmarking 21 dense supervision methods across four diverse environments and seven methodological families, with over 1.2K evaluation experiments across six open-weight model backbones. We find that simple prompting baselines consistently outperform recent dense supervision methods from the literature, and that performance clusters strongly by family. These findings hold across model sizes, environments, and observation modalities. QVal is designed to be easily extensible to new environments and methods, enabling researchers to iterate on dense supervision methods before any training run.

Reinforcement Learning (RL) plays a crucial role in aligning large language models (LLMs) with human preferences and improving their ability to perform complex tasks. However, current approaches either require significant computational resources due to the use of multiple models and extensive online sampling for training (e.g., PPO) or are framed as bandit problems (e.g., DPO, DRO), which often struggle with multi-step reasoning tasks, such as math problem-solving and complex reasoning that involve long chains of thought. To overcome these limitations, we introduce Direct Q-function Optimization (DQO), which formulates the response generation process as a Markov Decision Process (MDP) and utilizes the soft actor-critic (SAC) framework to optimize a Q-function directly parameterized by the language model. The MDP formulation of DQO offers structural advantages over bandit-based methods, enabling more effective process supervision. Experimental results on two math problem-solving datasets, GSM8K and MATH, demonstrate that DQO outperforms previous methods, establishing it as a promising offline reinforcement learning approach for aligning language models.

After the recent groundbreaking results of AlphaGo and AlphaZero, we have seen strong interests in deep reinforcement learning and artificial general intelligence (AGI) in game playing. However, deep learning is resource-intensive and the theory is not yet well developed. For small games, simple classical table-based Q-learning might still be the algorithm of choice. General Game Playing (GGP) provides a good testbed for reinforcement learning to research AGI. Q-learning is one of the canonical reinforcement learning methods, and has been used by (Banerjee & Stone, IJCAI 2007) in GGP. In this paper we implement Q-learning in GGP for three small-board games (Tic-Tac-Toe, Connect Four, Hex)source code: https://github.com/wh1992v/ggp-rl, to allow comparison to Banerjee et al.. We find that Q-learning converges to a high win rate in GGP. For the ε-greedy strategy, we propose a first enhancement, the dynamic ε algorithm. In addition, inspired by (Gelly & Silver, ICML 2007) we combine online search (Monte Carlo Search) to enhance offline learning, and propose QM-learning for GGP. Both enhancements improve the performance of classical Q-learning. In this work, GGP allows us to show, if augmented by appropriate enhancements, that classical table-based Q-learning can perform well in small games.

Parameterised actions in reinforcement learning are composed of discrete actions with continuous action-parameters. This provides a framework for solving complex domains that require combining high-level actions with flexible control. The recent P-DQN algorithm extends deep Q-networks to learn over such action spaces. However, it treats all action-parameters as a single joint input to the Q-network, invalidating its theoretical foundations. We analyse the issues with this approach and propose a novel method, multi-pass deep Q-networks, or MP-DQN, to address them. We empirically demonstrate that MP-DQN significantly outperforms P-DQN and other previous algorithms in terms of data efficiency and converged policy performance on the Platform, Robot Soccer Goal, and Half Field Offense domains.

We propose Flow-Anchored Noise-conditioned Q-Learning (FAN), a highly efficient and high-performing offline reinforcement learning (RL) algorithm. Recent work has shown that expressive flow policies and distributional critics improve offline RL performance, but at a high computational cost. Specifically, flow policies require iterative sampling to produce a single action, and distributional critics require computation over multiple samples (e.g., quantiles) to estimate value. To address these inefficiencies while maintaining high performance, we introduce FAN. Our method employs a behavior regularization technique that utilizes only a single flow policy iteration and requires only a single Gaussian noise sample for distributional critics. Our theoretical analysis of convergence and performance bounds demonstrates that these simplifications not only improve efficiency but also lead to superior task performance. Experiments on robotic manipulation and locomotion tasks demonstrate that FAN achieves state-of-the-art performance while significantly reducing both training and inference runtimes. We release our code at https://github.com/brianlsy98/FAN.

Large Language Models (LLMs) have shown impressive reasoning capabilities in well-defined problems with clear solutions, such as mathematics and coding. However, they still struggle with complex real-world scenarios like business negotiations, which require strategic reasoning-an ability to navigate dynamic environments and align long-term goals amidst uncertainty. Existing methods for strategic reasoning face challenges in adaptability, scalability, and transferring strategies to new contexts. To address these issues, we propose explicit policy optimization (EPO) for strategic reasoning, featuring an LLM that provides strategies in open-ended action space and can be plugged into arbitrary LLM agents to motivate goal-directed behavior. To improve adaptability and policy transferability, we train the strategic reasoning model via multi-turn reinforcement learning (RL) using process rewards and iterative self-play, without supervised fine-tuning (SFT) as a preliminary step. Experiments across social and physical domains demonstrate EPO's ability of long-term goal alignment through enhanced strategic reasoning, achieving state-of-the-art performance on social dialogue and web navigation tasks. Our findings reveal various collaborative reasoning mechanisms emergent in EPO and its effectiveness in generating novel strategies, underscoring its potential for strategic reasoning in real-world applications.

In long-horizon LLM agent reinforcement learning, weak policies often repeat similar failures, producing uninformative rollout trajectories and limiting effective policy optimization. Existing skill-centric methods improve exploration by optimizing, filtering, or internalizing reusable skills. However, they remain centered on the skills themselves rather than being designed as adaptive training-time support for the evolving policy. To address this, we propose a policy-centric training paradigm that reframes skills as a dynamic training scaffold. Our framework, Pats, converts rollout groups from the latest policy into evidence cards and uses task-specific evaluation to adjust the context used in subsequent rollouts. Concrete guidance helps weak policies to complete challenging tasks. As policy improves, redundant context is revised or removed to reduce reliance on explicit guidance while preserving useful rollout variation. The policy is optimized with environmental rewards using standard RLVR, and the training scaffold is discarded at deployment. On ALFWorld and WebShop, Pats improves over strong baselines by up to 18.6%. Across seven search-augmented QA benchmarks, it remains competitive while using 32.1% fewer prompt tokens than the baseline.

The rapid advancement of Large Language Models (LLMs) is revolutionizing AI for Games by enabling open-ended and fluid interactive storytelling. However, existing research has largely overlooked the critical challenge of maintaining long-horizon logical consistency and narrative integrity against unconstrained user interventions. To address this, we formulate this challenge as Narrative Commitment Preservation (NCP), and take interactive narrative as our testbed. We introduce NCP-Bench, a benchmark of 100 narrative environments derived from movie synopses. Each environment includes a structured narrative specification (trajectory, commitments, and initial facts) that we can automatically check throughout the interaction between the player agent and the narrator agent. Experiments across state-of-the-art LLMs reveal a substantial long-horizon consistency gap: high linguistic quality does not guarantee commitment preservation; even strong models frequently generate logically conflicting content under adversarial interventions, with the best-performing model (GPT-5.2) achieving only 42% survival rate after 20 turns and fact conflict rates ranging from 40% to 68% across models, and only isolated runs satisfying all achievement commitments within the 100-turn limit.

In lifelong learning, an agent learns throughout its entire life without resets, in a constantly changing environment, as we humans do. Consequently, lifelong learning comes with a plethora of research problems such as continual domain shifts, which result in non-stationary rewards and environment dynamics. These non-stationarities are difficult to detect and cope with due to their continuous nature. Therefore, exploration strategies and learning methods are required that are capable of tracking the steady domain shifts, and adapting to them. We propose Reactive Exploration to track and react to continual domain shifts in lifelong reinforcement learning, and to update the policy correspondingly. To this end, we conduct experiments in order to investigate different exploration strategies. We empirically show that representatives of the policy-gradient family are better suited for lifelong learning, as they adapt more quickly to distribution shifts than Q-learning. Thereby, policy-gradient methods profit the most from Reactive Exploration and show good results in lifelong learning with continual domain shifts. Our code is available at: https://github.com/ml-jku/reactive-exploration.

We propose training fitted Q-iteration with log-loss (FQI-LOG) for batch reinforcement learning (RL). We show that the number of samples needed to learn a near-optimal policy with FQI-LOG scales with the accumulated cost of the optimal policy, which is zero in problems where acting optimally achieves the goal and incurs no cost. In doing so, we provide a general framework for proving small-cost bounds, i.e. bounds that scale with the optimal achievable cost, in batch RL. Moreover, we empirically verify that FQI-LOG uses fewer samples than FQI trained with squared loss on problems where the optimal policy reliably achieves the goal.

Generative policies based on expressive model classes, such as diffusion and flow matching, are well-suited to complex control problems with highly multimodal action distributions. Their expressivity, however, comes at a significant inference cost: generating each action typically requires simulating many steps of the generative process, compounding latency across sequential decision-making rollouts. We introduce flow map policies, a novel class of generative policies designed for fast action generation by learning to take arbitrary-size jumps including one-step jumps-across the generative dynamics of existing flow-based policies. We instantiate flow map policies for offline-to-online reinforcement learning (RL) and formulate online adaptation as a trust-region optimization problem that improves the critic's Q-value while remaining close to the offline policy. We theoretically derive FLOW MAP Q-GUIDANCE (FMQ), a principled closed-form learning target that is optimal for adapting offline flow map policies under a critic-guided trust-region constraint. We further introduce Q-GUIDED BEAM SEARCH (QGBS), a stochastic flow-map sampler that combines renoising with beam search to enable iterative inference-time refinement. Across 12 challenging robotic manipulation and locomotion tasks from OGBench and RoboMimic, FMQ achieves state-of-the-art performance in offline-to-online RL, outperforming the previous one-step policy MVP by a relative improvement of 21.3% on the average success rate.

The recent advancement of Large Language Models (LLMs) has established their potential as autonomous interactive agents. However, they often struggle in strategic games of incomplete information, such as bilateral price negotiation. In this paper, we investigate if Reinforcement Learning from Verifiable Rewards (RLVR) can effectively teach LLMs to negotiate. Specifically, we explore the strategic behaviors that emerge during the learning process. We introduce a framework that trains a mid-sized buyer agent against a regulated LLM seller across a wide distribution of real-world products. By grounding reward signals directly in the maximization of economic surplus and strict adherence to private budget constraints, we reveal a novel four-phase strategic evolution. The agent progresses from naive bargaining to using aggressive starting prices, moves through a phase of deadlock, and ultimately develops sophisticated persuasive skills. Our results demonstrate that this verifiable training allows a 30B agent to significantly outperform frontier models over ten times its size in extracting surplus. Furthermore, the trained agent generalizes robustly to stronger counterparties unseen during training and remains effective even when facing hostile, adversarial seller personas.

In many real-world settings, a team of agents must coordinate their behaviour while acting in a decentralised way. At the same time, it is often possible to train the agents in a centralised fashion in a simulated or laboratory setting, where global state information is available and communication constraints are lifted. Learning joint action-values conditioned on extra state information is an attractive way to exploit centralised learning, but the best strategy for then extracting decentralised policies is unclear. Our solution is QMIX, a novel value-based method that can train decentralised policies in a centralised end-to-end fashion. QMIX employs a network that estimates joint action-values as a complex non-linear combination of per-agent values that condition only on local observations. We structurally enforce that the joint-action value is monotonic in the per-agent values, which allows tractable maximisation of the joint action-value in off-policy learning, and guarantees consistency between the centralised and decentralised policies. We evaluate QMIX on a challenging set of StarCraft II micromanagement tasks, and show that QMIX significantly outperforms existing value-based multi-agent reinforcement learning methods.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising approach to improve the reasoning abilities of Large Language Models (LLMs). Among RLVR algorithms, Group Relative Policy Optimization (GRPO) and its variants have demonstrated strong performance and high training efficiency. However, GRPO-style objectives exhibit two issues on high accuracy prompts including mastered prompts (rollout accuracy =1) and majority-correct prompts (rollout accuracy in (0.5,1)). For mastered prompts, group-relative advantages vanish, yielding no training signal and unconstrained policy drift that can cause forgetting. For majority-correct prompts, the induced query weight shrinks as accuracy increases, weakening consolidation from partial correctness to mastery. To alleviate this, we propose Mastery-Consolidated Policy Optimization (MCPO), which introduces (i) a hinge-KL regularizer applied exclusively to mastered prompts to bound harmful policy drift between successive gradient steps, and (ii) a weighting mechanism that prioritizes majority-correct prompts to better allocate optimization effort. Extensive experiments across three mathematical benchmarks demonstrate that MCPO consistently improves pass@1 performance. Counter-intuitively, rather than restricting exploration, MCPO boosts pass@k metrics, indicating that mastery consolidation further catalyzes solution diversity.

Reinforcement Learning (RL) agents often struggle with efficiency and performance in complex environments. We propose a novel framework that uses a Large Language Model (LLM) to dynamically generate a curriculum over available actions, enabling the agent to incorporate each action individually. We apply this framework to the game of Blackjack, where the LLM creates a multi-stage training path that progressively introduces complex actions to a Tabular Q-Learning and a Deep Q-Network (DQN) agent. Our evaluation in a realistic 8-deck simulation over 10 independent runs demonstrates significant performance gains over standard training methods. The curriculum-based approach increases the DQN agent's average win rate from 43.97% to 47.41%, reduces the average bust rate from 32.9% to 28.0%, and accelerates the overall workflow by over 74%, with the agent's full training completing faster than the baseline's evaluation phase alone. These results validate that LLM-guided curricula can build more effective, robust, and efficient RL agents.

Real-world reinforcement learning (RL) is often severely limited since typical RL algorithms heavily rely on the reset mechanism to sample proper initial states. In practice, the reset mechanism is expensive to implement due to the need for human intervention or heavily engineered environments. To make learning more practical, we propose a generic no-regret reduction to systematically design reset-free RL algorithms. Our reduction turns reset-free RL into a two-player game. We show that achieving sublinear regret in this two-player game would imply learning a policy that has both sublinear performance regret and sublinear total number of resets in the original RL problem. This means that the agent eventually learns to perform optimally and avoid resets. By this reduction, we design an instantiation for linear Markov decision processes, which is the first provably correct reset-free RL algorithm to our knowledge.

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.

The popular Q-learning algorithm is known to overestimate action values under certain conditions. It was not previously known whether, in practice, such overestimations are common, whether they harm performance, and whether they can generally be prevented. In this paper, we answer all these questions affirmatively. In particular, we first show that the recent DQN algorithm, which combines Q-learning with a deep neural network, suffers from substantial overestimations in some games in the Atari 2600 domain. We then show that the idea behind the Double Q-learning algorithm, which was introduced in a tabular setting, can be generalized to work with large-scale function approximation. We propose a specific adaptation to the DQN algorithm and show that the resulting algorithm not only reduces the observed overestimations, as hypothesized, but that this also leads to much better performance on several games.

While a number of existing approaches for building foundation model agents rely on prompting or fine-tuning with human demonstrations, it is not sufficient in dynamic environments (e.g., mobile device control). On-policy reinforcement learning (RL) should address these limitations, but collecting actual rollouts in an environment is often undesirable in truly open-ended agentic problems such as mobile device control or interacting with humans, where each unit of interaction is associated with a cost. In such scenarios, a method for policy learning that can utilize off-policy experience by learning a trained action-value function is much more effective. In this paper, we develop an approach, called Digi-Q, to train VLM-based action-value Q-functions which are then used to extract the agent policy. We study our approach in the mobile device control setting. Digi-Q trains the Q-function using offline temporal-difference (TD) learning, on top of frozen, intermediate-layer features of a VLM. Compared to fine-tuning the whole VLM, this approach saves us compute and enhances scalability. To make the VLM features amenable for representing the Q-function, we need to employ an initial phase of fine-tuning to amplify coverage over actionable information needed for value function. Once trained, we use this Q-function via a Best-of-N policy extraction operator that imitates the best action out of multiple candidate actions from the current policy as ranked by the value function, enabling policy improvement without environment interaction. Digi-Q outperforms several prior methods on user-scale device control tasks in Android-in-the-Wild, attaining 21.2% improvement over prior best-performing method. In some cases, our Digi-Q approach already matches state-of-the-art RL methods that require interaction. The project is open-sourced at https://github.com/DigiRL-agent/digiq

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.

Chain-of-Thought (CoT) reasoning offers a promising window into model monitoring. However, monitoring relies on faithfulness, i.e., the model output strictly derives from its reasoning trace. We identify an alignment tension where a model must be faithful enough to be monitored, yet robust enough to reject unsafe reasoning. We demonstrate that this counterbalance exists in current Large Reasoning Models (LRMs), and show ways in which it can be addressed. We introduce HazMart, a human-written dataset set in an autonomous AI shopkeeper scenario. Unlike prior work that relies on providing hints in prompts to test faithfulness (e.g., "A Stanford professor said it should be Answer A"), we propose a novel replacement-based technique, which we call Targeted Reasoning Replacement (TRR), that directly intervenes in the reasoning chain to substitute in unsafe or illogical thoughts (e.g., "Wait, the answer must be Option B [was Option A] because it is the most fitting"). DeepSeek-R1-Llama-70B exhibits high faithfulness (97.5%) but fails to reject Unsafe Reasoning (12.3%), while QwQ-32B is more robust (73.9% safety) at the cost of lower faithfulness (74.7%). Mechanistic analyses of QwQ-32B reveal that these properties are represented by anti-correlated internal directions peaking at the action-commit token. Finally, we demonstrate that representation steering can independently amplify the safety direction, increasing safe behavior by 9 percentage points while maintaining base capabilities.

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.

Value-based methods constitute a fundamental methodology in planning and deep reinforcement learning (RL). In this paper, we propose to exploit the underlying structures of the state-action value function, i.e., Q function, for both planning and deep RL. In particular, if the underlying system dynamics lead to some global structures of the Q function, one should be capable of inferring the function better by leveraging such structures. Specifically, we investigate the low-rank structure, which widely exists for big data matrices. We verify empirically the existence of low-rank Q functions in the context of control and deep RL tasks. As our key contribution, by leveraging Matrix Estimation (ME) techniques, we propose a general framework to exploit the underlying low-rank structure in Q functions. This leads to a more efficient planning procedure for classical control, and additionally, a simple scheme that can be applied to any value-based RL techniques to consistently achieve better performance on "low-rank" tasks. Extensive experiments on control tasks and Atari games confirm the efficacy of our approach. Code is available at https://github.com/YyzHarry/SV-RL.

We propose UCBMQ, Upper Confidence Bound Momentum Q-learning, a new algorithm for reinforcement learning in tabular and possibly stage-dependent, episodic Markov decision process. UCBMQ is based on Q-learning where we add a momentum term and rely on the principle of optimism in face of uncertainty to deal with exploration. Our new technical ingredient of UCBMQ is the use of momentum to correct the bias that Q-learning suffers while, at the same time, limiting the impact it has on the second-order term of the regret. For UCBMQ, we are able to guarantee a regret of at most O(H^3SAT+ H^4 S A ) where H is the length of an episode, S the number of states, A the number of actions, T the number of episodes and ignoring terms in poly-log(SAHT). Notably, UCBMQ is the first algorithm that simultaneously matches the lower bound of Ω(H^3SAT) for large enough T and has a second-order term (with respect to the horizon T) that scales only linearly with the number of states S.

Methods for learning from demonstration (LfD) have shown success in acquiring behavior policies by imitating a user. However, even for a single task, LfD may require numerous demonstrations. For versatile agents that must learn many tasks via demonstration, this process would substantially burden the user if each task were learned in isolation. To address this challenge, we introduce the novel problem of lifelong learning from demonstration, which allows the agent to continually build upon knowledge learned from previously demonstrated tasks to accelerate the learning of new tasks, reducing the amount of demonstrations required. As one solution to this problem, we propose the first lifelong learning approach to inverse reinforcement learning, which learns consecutive tasks via demonstration, continually transferring knowledge between tasks to improve performance.

Search agents have emerged as a pivotal paradigm for solving open-ended, knowledge-intensive reasoning tasks. However, training these agents via Reinforcement Learning (RL) faces a critical dilemma: interacting with live commercial Web APIs is prohibitively expensive, while relying on static data snapshots often introduces noise due to data misalignment. This misalignment generates corrupted reward signals that destabilize training by penalizing correct reasoning or rewarding hallucination. To address this, we propose SearchGym, a simulation environment designed to bootstrap robust search agents. SearchGym employs a rigorous generative pipeline to construct a verifiable knowledge graph and an aligned document corpus, ensuring that every reasoning task is factually grounded and strictly solvable. Building on this controllable environment, we introduce SearchGym-RL, a curriculum learning methodology that progressively optimizes agent policies through purified feedback, evolving from basic interactions to complex, long-horizon planning. Extensive experiments across the Llama and Qwen families demonstrate strong Sim-to-Real generalization. Notably, our Qwen2.5-7B-Base model trained within SearchGym surpasses the web-enhanced ASearcher baseline across nine diverse benchmarks by an average relative margin of 10.6%. Our results validate that high-fidelity simulation serves as a scalable and highly cost-effective methodology for developing capable search agents.

When reward functions are hand-designed, deep reinforcement learning algorithms often suffer from reward misspecification, causing them to learn suboptimal policies in terms of the intended task objectives. In the single-agent case, inverse reinforcement learning (IRL) techniques attempt to address this issue by inferring the reward function from expert demonstrations. However, in multi-agent problems, misalignment between the learned and true objectives is exacerbated due to increased environment non-stationarity and variance that scales with multiple agents. As such, in multi-agent general-sum games, multi-agent IRL algorithms have difficulty balancing cooperative and competitive objectives. To address these issues, we propose Multi-Agent Marginal Q-Learning from Demonstrations (MAMQL), a novel sample-efficient framework for multi-agent IRL. For each agent, MAMQL learns a critic marginalized over the other agents' policies, allowing for a well-motivated use of Boltzmann policies in the multi-agent context. We identify a connection between optimal marginalized critics and single-agent soft-Q IRL, allowing us to apply a direct, simple optimization criterion from the single-agent domain. Across our experiments on three different simulated domains, MAMQL significantly outperforms previous multi-agent methods in average reward, sample efficiency, and reward recovery by often more than 2-5x. We make our code available at https://sites.google.com/view/mamql .

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.

Building open-ended learning agents involves challenges in pre-trained language model (LLM) and reinforcement learning (RL) approaches. LLMs struggle with context-specific real-time interactions, while RL methods face efficiency issues for exploration. To this end, we propose OpenContra, a co-training framework that cooperates LLMs and GRL to construct an open-ended agent capable of comprehending arbitrary human instructions. The implementation comprises two stages: (1) fine-tuning an LLM to translate human instructions into structured goals, and curriculum training a goal-conditioned RL policy to execute arbitrary goals; (2) collaborative training to make the LLM and RL policy learn to adapt each, achieving open-endedness on instruction space. We conduct experiments on Contra, a battle royale FPS game with a complex and vast goal space. The results show that an agent trained with OpenContra comprehends arbitrary human instructions and completes goals with a high completion ratio, which proves that OpenContra may be the first practical solution for constructing open-ended embodied agents.

We introduce a novel reinforcement learning framework of LLM agents named AGILE (AGent that Interacts and Learns from Environments) designed to perform complex conversational tasks with users, leveraging LLMs, memory, tools, and interactions with experts. The agent possesses capabilities beyond conversation, including reflection, tool usage, and expert consultation. We formulate the construction of such an LLM agent as a reinforcement learning (RL) problem, in which the LLM serves as the policy model. We fine-tune the LLM using labeled data of actions and the PPO algorithm. We focus on question answering and release a dataset for agents called ProductQA, comprising challenging questions in online shopping. Our extensive experiments on ProductQA, MedMCQA and HotPotQA show that AGILE agents based on 7B and 13B LLMs trained with PPO can outperform GPT-4 agents. Our ablation study highlights the indispensability of memory, tools, consultation, reflection, and reinforcement learning in achieving the agent's strong performance. Datasets and code are available at https://github.com/bytarnish/AGILE.

Successor Features (SF) combined with Generalized Policy Improvement (GPI) provide a robust framework for transfer learning in Reinforcement Learning (RL) by decoupling environment dynamics from reward functions. However, standard SF learning methods typically rely on semi-gradient Temporal Difference (TD) updates. When combined with non-linear function approximation, semi-gradient methods lack robust convergence guarantees and can lead to instability, particularly in the multi-task setting where accurate feature estimation is critical for effective GPI. Inspired by Full Gradient DQN, we propose Full-Gradient Successor Feature Representations Q-Learning (FG-SFRQL), an algorithm that optimizes the successor features by minimizing the full Mean Squared Bellman Error. Unlike standard approaches, our method computes gradients with respect to parameters in both the online and target networks. We provide a theoretical proof of almost-sure convergence for FG-SFRQL and demonstrate empirically that minimizing the full residual leads to superior sample efficiency and transfer performance compared to semi-gradient baselines in both discrete and continuous domains.

Large language models (LLMs) show strong capabilities in general reasoning but typically lack reliability in scientific domains like quantum mechanics, which demand strict adherence to physical constraints. This limitation arises from the scarcity of verifiable training resources and the inadequacy of coarse feedback signals in standard alignment paradigms. To address the data challenge, we introduce QuantumQA, a large-scale dataset constructed via a task-adaptive strategy and a hybrid verification protocol that combines deterministic solvers with semantic auditing to guarantee scientific rigor. Building on this foundation, we propose the verification-aware reward model (VRM) tailored for Reinforcement Learning with Verifiable Rewards (RLVR), which employs an adaptive reward fusion (ARF) mechanism to dynamically integrate deterministic signals from a scientific execution suite (SES) with multidimensional semantic evaluations for precise supervision. Experimental results demonstrate that our method consistently outperforms baselines and general-purpose preference models. Notably, our optimized 8B model achieves performance competitive with proprietary models, validating that incorporating verifiable, rule-based feedback into the reinforcement learning loop offers a parameter-efficient alternative to pure scaling.

Widely-used deep reinforcement learning algorithms have been shown to fail in the batch setting--learning from a fixed data set without interaction with the environment. Following this result, there have been several papers showing reasonable performances under a variety of environments and batch settings. In this paper, we benchmark the performance of recent off-policy and batch reinforcement learning algorithms under unified settings on the Atari domain, with data generated by a single partially-trained behavioral policy. We find that under these conditions, many of these algorithms underperform DQN trained online with the same amount of data, as well as the partially-trained behavioral policy. To introduce a strong baseline, we adapt the Batch-Constrained Q-learning algorithm to a discrete-action setting, and show it outperforms all existing algorithms at this task.

Natural intelligence processes experience as a continuous stream, sensing, acting, and learning moment-by-moment in real time. Streaming learning, the modus operandi of classic reinforcement learning (RL) algorithms like Q-learning and TD, mimics natural learning by using the most recent sample without storing it. This approach is also ideal for resource-constrained, communication-limited, and privacy-sensitive applications. However, in deep RL, learners almost always use batch updates and replay buffers, making them computationally expensive and incompatible with streaming learning. Although the prevalence of batch deep RL is often attributed to its sample efficiency, a more critical reason for the absence of streaming deep RL is its frequent instability and failure to learn, which we refer to as stream barrier. This paper introduces the stream-x algorithms, the first class of deep RL algorithms to overcome stream barrier for both prediction and control and match sample efficiency of batch RL. Through experiments in Mujoco Gym, DM Control Suite, and Atari Games, we demonstrate stream barrier in existing algorithms and successful stable learning with our stream-x algorithms: stream Q, stream AC, and stream TD, achieving the best model-free performance in DM Control Dog environments. A set of common techniques underlies the stream-x algorithms, enabling their success with a single set of hyperparameters and allowing for easy extension to other algorithms, thereby reviving streaming RL.

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.

Recent advances in automated theorem proving (ATP) through LLMs have highlighted the potential of formal reasoning with Lean 4 codes. However, ATP has not yet be revolutionized by the recent posttraining scaling as demonstrated by Open AI O1/O3 and Deepseek R1. In this work, we investigate the entire posttraining of ATP, aiming to align it with breakthroughs in reasoning models in natural languages.To begin, we continual train current ATP models with a hybrid dataset, which consists of numerous statement-proof pairs, and additional data aimed at incorporating cognitive behaviors that emulate human reasoning and hypothesis refinement. Next, we explore reinforcement learning with the use of outcome reward returned by Lean 4 compiler. Through our designed continual training and reinforcement learning processes, we have successfully improved existing formal provers, including both DeepSeek-Prover-v1.5 and Goedel-Prover, achieving state-of-the-art performance in the field of whole-proof generation. For example, we achieve a 59.8% pass rate (pass@32) on MiniF2F. This is an on-going project and we will progressively update our findings, release our data and training details.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising paradigm for post-training reasoning models. However, group-based methods such as Group Relative Policy Optimization (GRPO) face a critical dilemma in sparse-reward settings: pure Reinforcement Learning (RL) suffers from advantage collapse and high-variance gradient estimation, while mixed-policy optimization introduces persistent distributional bias. To resolve this dilemma, we introduce Hindsight-Anchored Policy Optimization (HAPO). HAPO employs the Synthetic Success Injection (SSI) operator, a hindsight mechanism that selectively anchors optimization to teacher demonstrations during failure. This injection is governed by a Thompson sampling-inspired gating mechanism, creating an autonomous, self-paced curriculum. Theoretically, we demonstrate that HAPO achieves asymptotic consistency: by naturally annealing the teacher signal as the policy improves, HAPO recovers the unbiased on-policy gradient. This ensures off-policy guidance acts as a temporary scaffold rather than a persistent ceiling, enabling the model to surpass the limitations of static teacher forcing.

Model-based representations recently stand out as a promising framework that embeds latent dynamics information into the representations for downstream off-policy actor-critic learning. It implicitly combines the advantages of both model-free and model-based approaches while avoiding the training costs associated with model-based methods. Nevertheless, existing model-based representation methods can fail to capture sufficient information about relevant variables and can overfit to early experiences in the replay buffer. These incur biases in representation and actor-critic learning, leading to inferior performance. To address this, we propose Debiased model-based Representations for Q-learning, tagged DR.Q algorithm. DR.Q explicitly maximizes the mutual information between the representations of the current state-action pair and the next state besides minimizing their deviations, and samples transitions with faded prioritized experience replay. We evaluate DR.Q on numerous continuous control benchmarks with a single set of hyperparameters, and the results demonstrate that DR.Q can match or surpass recent strong baselines, sometimes outperforming them by a large margin. Our code is available at https://github.com/dmksjfl/DR.Q.

In this work we create agents that can perform well beyond a single, individual task, that exhibit much wider generalisation of behaviour to a massive, rich space of challenges. We define a universe of tasks within an environment domain and demonstrate the ability to train agents that are generally capable across this vast space and beyond. The environment is natively multi-agent, spanning the continuum of competitive, cooperative, and independent games, which are situated within procedurally generated physical 3D worlds. The resulting space is exceptionally diverse in terms of the challenges posed to agents, and as such, even measuring the learning progress of an agent is an open research problem. We propose an iterative notion of improvement between successive generations of agents, rather than seeking to maximise a singular objective, allowing us to quantify progress despite tasks being incomparable in terms of achievable rewards. We show that through constructing an open-ended learning process, which dynamically changes the training task distributions and training objectives such that the agent never stops learning, we achieve consistent learning of new behaviours. The resulting agent is able to score reward in every one of our humanly solvable evaluation levels, with behaviour generalising to many held-out points in the universe of tasks. Examples of this zero-shot generalisation include good performance on Hide and Seek, Capture the Flag, and Tag. Through analysis and hand-authored probe tasks we characterise the behaviour of our agent, and find interesting emergent heuristic behaviours such as trial-and-error experimentation, simple tool use, option switching, and cooperation. Finally, we demonstrate that the general capabilities of this agent could unlock larger scale transfer of behaviour through cheap finetuning.

As the use of cloud computing continues to rise, controlling cost becomes increasingly important. Yet there is evidence that 30\% - 45\% of cloud spend is wasted. Existing tools for cloud provisioning typically rely on highly trained human experts to specify what to monitor, thresholds for triggering action, and actions. In this paper we explore the use of reinforcement learning (RL) to acquire policies to balance performance and spend, allowing humans to specify what they want as opposed to how to do it, minimizing the need for cloud expertise. Empirical results with tabular, deep, and dueling double deep Q-learning with the CloudSim simulator show the utility of RL and the relative merits of the approaches. We also demonstrate effective policy transfer learning from an extremely simple simulator to CloudSim, with the next step being transfer from CloudSim to an Amazon Web Services physical environment.

Pretraining navigation diffusion policies rely on large-scale expert demonstrations. These data are typically generated by a fully-informed oracle planner suited to a single nominal robot. This limits the policy's generalization to diverse embodiments and challenging scenarios (e.g., escaping dead ends or detouring long obstacles) that demand diverse local reactive behaviors with only onboard local observations. Post-training the policy with reinforcement learning (RL) offers a principled remedy. However, previous RL for diffusion approaches lead to only marginal improvements. This is because the intractable likelihood of diffusion policies renders policy gradients unstable in addition to inefficient policy exploration. To address these challenges, we propose a data-efficient diffusion RL post-training framework - GQRM (Group Q-score Reweighted Matching). Our framework introduces two complementary designs: (i) a self-bootstrapped exploration strategy with behavior perturbation that preserves the pretrained policy prior, and (ii) a group Q-score normalization mechanism that computes per-trajectory values on each state for efficient reweighted score matching. By conducting distributed online RL training across heterogeneous embodiments, the resulting fine-tuned policy, X-NavDP, achieves state-of-the-art cross-embodiment visual navigation performance, improving the overall success rate from 61.20% to 84.28% in simulation and 10% to 65% in real-world hard cases. The code and model are publicly available at https://yty-sky.github.io/x-navdp-project-page.

Credit assignment, the process of attributing credit or blame to individual agents for their contributions to a team's success or failure, remains a fundamental challenge in multi-agent reinforcement learning (MARL), particularly in environments with sparse rewards. Commonly-used approaches such as value decomposition often lead to suboptimal policies in these settings, and designing dense reward functions that align with human intuition can be complex and labor-intensive. In this work, we propose a novel framework where a large language model (LLM) generates dense, agent-specific rewards based on a natural language description of the task and the overall team goal. By learning a potential-based reward function over multiple queries, our method reduces the impact of ranking errors while allowing the LLM to evaluate each agent's contribution to the overall task. Through extensive experiments, we demonstrate that our approach achieves faster convergence and higher policy returns compared to state-of-the-art MARL baselines.

In reinforcement learning (RL), an agent learns to perform a task by interacting with an environment and receiving feedback (a numerical reward) for its actions. However, the assumption that rewards are always observable is often not applicable in real-world problems. For example, the agent may need to ask a human to supervise its actions or activate a monitoring system to receive feedback. There may even be a period of time before rewards become observable, or a period of time after which rewards are no longer given. In other words, there are cases where the environment generates rewards in response to the agent's actions but the agent cannot observe them. In this paper, we formalize a novel but general RL framework - Monitored MDPs - where the agent cannot always observe rewards. We discuss the theoretical and practical consequences of this setting, show challenges raised even in toy environments, and propose algorithms to begin to tackle this novel setting. This paper introduces a powerful new formalism that encompasses both new and existing problems and lays the foundation for future research.

Using a high Update-To-Data (UTD) ratio, model-based methods have recently achieved much higher sample efficiency than previous model-free methods for continuous-action DRL benchmarks. In this paper, we introduce a simple model-free algorithm, Randomized Ensembled Double Q-Learning (REDQ), and show that its performance is just as good as, if not better than, a state-of-the-art model-based algorithm for the MuJoCo benchmark. Moreover, REDQ can achieve this performance using fewer parameters than the model-based method, and with less wall-clock run time. REDQ has three carefully integrated ingredients which allow it to achieve its high performance: (i) a UTD ratio >> 1; (ii) an ensemble of Q functions; (iii) in-target minimization across a random subset of Q functions from the ensemble. Through carefully designed experiments, we provide a detailed analysis of REDQ and related model-free algorithms. To our knowledge, REDQ is the first successful model-free DRL algorithm for continuous-action spaces using a UTD ratio >> 1.

For sophisticated reinforcement learning (RL) systems to interact usefully with real-world environments, we need to communicate complex goals to these systems. In this work, we explore goals defined in terms of (non-expert) human preferences between pairs of trajectory segments. We show that this approach can effectively solve complex RL tasks without access to the reward function, including Atari games and simulated robot locomotion, while providing feedback on less than one percent of our agent's interactions with the environment. This reduces the cost of human oversight far enough that it can be practically applied to state-of-the-art RL systems. To demonstrate the flexibility of our approach, we show that we can successfully train complex novel behaviors with about an hour of human time. These behaviors and environments are considerably more complex than any that have been previously learned from human feedback.

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

Tremendous progress has been made in reinforcement learning (RL) over the past decade. Most of these advancements came through the continual development of new algorithms, which were designed using a combination of mathematical derivations, intuitions, and experimentation. Such an approach of creating algorithms manually is limited by human understanding and ingenuity. In contrast, meta-learning provides a toolkit for automatic machine learning method optimisation, potentially addressing this flaw. However, black-box approaches which attempt to discover RL algorithms with minimal prior structure have thus far not outperformed existing hand-crafted algorithms. Mirror Learning, which includes RL algorithms, such as PPO, offers a potential middle-ground starting point: while every method in this framework comes with theoretical guarantees, components that differentiate them are subject to design. In this paper we explore the Mirror Learning space by meta-learning a "drift" function. We refer to the immediate result as Learnt Policy Optimisation (LPO). By analysing LPO we gain original insights into policy optimisation which we use to formulate a novel, closed-form RL algorithm, Discovered Policy Optimisation (DPO). Our experiments in Brax environments confirm state-of-the-art performance of LPO and DPO, as well as their transfer to unseen settings.

Through reinforcement learning with verifiable rewards (RLVR), large language models have achieved substantial progress in domains with easily verifiable outcomes, such as mathematics and coding. However, when applied to more complex tasks like open-domain question answering, RLVR faces significant challenges due to the difficulty of verifying correctness. The nuanced and ambiguous nature of real-world knowledge makes it difficult to reliably evaluate correctness in these settings, necessitating further abilities that extend beyond mere logical consistency to encompass an understanding and assessment of both external and internal knowledge. Recent work has primarily focused on improving faithfulness, defined as semantic alignment with supporting documents, which can cause models to rely excessively on external sources and diminish their capacity for critical assessment. To address this, we propose the Thinking-supervised Reward Model (TRM), which incorporates sentence-level thinking supervision to endow reward models with critical thinking abilities. Given a query, answer, and supporting documents, TRM first assesses the faithfulness of each answer sentence to the supporting documents, and then applies a reasoning step to evaluate sentence-level correctness. By structuring reward modeling as a sequence of faithfulness, reasoning, and correctness evaluations, TRM encourages models to critically assess and leverage both external and internal knowledge. Experiments on reward signals demonstrate that TRM substantially improves the identification of incorrect sentences, and incorporating TRM into policy optimization leads to significant gains in both answer correctness and usefulness.

This study presents a novel computer system performance optimization and adaptive workload management scheduling algorithm based on Q-learning. In modern computing environments, characterized by increasing data volumes, task complexity, and dynamic workloads, traditional static scheduling methods such as Round-Robin and Priority Scheduling fail to meet the demands of efficient resource allocation and real-time adaptability. By contrast, Q-learning, a reinforcement learning algorithm, continuously learns from system state changes, enabling dynamic scheduling and resource optimization. Through extensive experiments, the superiority of the proposed approach is demonstrated in both task completion time and resource utilization, outperforming traditional and dynamic resource allocation (DRA) algorithms. These findings are critical as they highlight the potential of intelligent scheduling algorithms based on reinforcement learning to address the growing complexity and unpredictability of computing environments. This research provides a foundation for the integration of AI-driven adaptive scheduling in future large-scale systems, offering a scalable, intelligent solution to enhance system performance, reduce operating costs, and support sustainable energy consumption. The broad applicability of this approach makes it a promising candidate for next-generation computing frameworks, such as edge computing, cloud computing, and the Internet of Things.

Language agents have become a promising solution to complex interactive tasks. One of the key ingredients to the success of language agents is the reward model on the trajectory of the agentic workflow, which provides valuable guidance during training or inference. However, due to the lack of annotations of intermediate interactions, most existing works use an outcome reward model to optimize policies across entire trajectories. This may lead to sub-optimal policies and hinder the overall performance. To address this, we propose QLASS (Q-guided Language Agent Stepwise Search), to automatically generate annotations by estimating Q-values in a stepwise manner for open language agents. By introducing a reasoning tree and performing process reward modeling, QLASS provides effective intermediate guidance for each step. With the stepwise guidance, we propose a Q-guided generation strategy to enable language agents to better adapt to long-term value, resulting in significant performance improvement during model inference on complex interactive agent tasks. Notably, even with almost half the annotated data, QLASS retains strong performance, demonstrating its efficiency in handling limited supervision. We also empirically demonstrate that QLASS can lead to more effective decision making through qualitative analysis. We will release our code and data.

The capability of continuously learning new skills via a sequence of pre-collected offline datasets is desired for an agent. However, consecutively learning a sequence of offline tasks likely leads to the catastrophic forgetting issue under resource-limited scenarios. In this paper, we formulate a new setting, continual offline reinforcement learning (CORL), where an agent learns a sequence of offline reinforcement learning tasks and pursues good performance on all learned tasks with a small replay buffer without exploring any of the environments of all the sequential tasks. For consistently learning on all sequential tasks, an agent requires acquiring new knowledge and meanwhile preserving old knowledge in an offline manner. To this end, we introduced continual learning algorithms and experimentally found experience replay (ER) to be the most suitable algorithm for the CORL problem. However, we observe that introducing ER into CORL encounters a new distribution shift problem: the mismatch between the experiences in the replay buffer and trajectories from the learned policy. To address such an issue, we propose a new model-based experience selection (MBES) scheme to build the replay buffer, where a transition model is learned to approximate the state distribution. This model is used to bridge the distribution bias between the replay buffer and the learned model by filtering the data from offline data that most closely resembles the learned model for storage. Moreover, in order to enhance the ability on learning new tasks, we retrofit the experience replay method with a new dual behavior cloning (DBC) architecture to avoid the disturbance of behavior-cloning loss on the Q-learning process. In general, we call our algorithm offline experience replay (OER). Extensive experiments demonstrate that our OER method outperforms SOTA baselines in widely-used Mujoco environments.

We seek to learn an effective policy for a Markov Decision Process (MDP) with continuous states via Q-Learning. Given a set of basis functions over state action pairs we search for a corresponding set of linear weights that minimizes the mean Bellman residual. Our algorithm uses a Kalman filter model to estimate those weights and we have developed a simpler approximate Kalman filter model that outperforms the current state of the art projected TD-Learning methods on several standard benchmark problems.

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

We initiate the study of Multi-Agent Reinforcement Learning from Human Feedback (MARLHF), exploring both theoretical foundations and empirical validations. We define the task as identifying Nash equilibrium from a preference-only offline dataset in general-sum games, a problem marked by the challenge of sparse feedback signals. Our theory establishes the upper complexity bounds for Nash Equilibrium in effective MARLHF, demonstrating that single-policy coverage is inadequate and highlighting the importance of unilateral dataset coverage. These theoretical insights are verified through comprehensive experiments. To enhance the practical performance, we further introduce two algorithmic techniques. (1) We propose a Mean Squared Error (MSE) regularization along the time axis to achieve a more uniform reward distribution and improve reward learning outcomes. (2) We utilize imitation learning to approximate the reference policy, ensuring stability and effectiveness in training. Our findings underscore the multifaceted approach required for MARLHF, paving the way for effective preference-based multi-agent systems.

We propose a reinforcement learning (RL) framework under a broad class of risk objectives, characterized by convex scoring functions. This class covers many common risk measures, such as variance, Expected Shortfall, entropic Value-at-Risk, and mean-risk utility. To resolve the time-inconsistency issue, we consider an augmented state space and an auxiliary variable and recast the problem as a two-state optimization problem. We propose a customized Actor-Critic algorithm and establish some theoretical approximation guarantees. A key theoretical contribution is that our results do not require the Markov decision process to be continuous. Additionally, we propose an auxiliary variable sampling method inspired by the alternating minimization algorithm, which is convergent under certain conditions. We validate our approach in simulation experiments with a financial application in statistical arbitrage trading, demonstrating the effectiveness of the algorithm.

Aiming to produce reinforcement learning (RL) policies that are human-interpretable and can generalize better to novel scenarios, Trivedi et al. (2021) present a method (LEAPS) that first learns a program embedding space to continuously parameterize diverse programs from a pre-generated program dataset, and then searches for a task-solving program in the learned program embedding space when given a task. Despite the encouraging results, the program policies that LEAPS can produce are limited by the distribution of the program dataset. Furthermore, during searching, LEAPS evaluates each candidate program solely based on its return, failing to precisely reward correct parts of programs and penalize incorrect parts. To address these issues, we propose to learn a meta-policy that composes a series of programs sampled from the learned program embedding space. By learning to compose programs, our proposed hierarchical programmatic reinforcement learning (HPRL) framework can produce program policies that describe out-of-distributionally complex behaviors and directly assign credits to programs that induce desired behaviors. The experimental results in the Karel domain show that our proposed framework outperforms baselines. The ablation studies confirm the limitations of LEAPS and justify our design choices.