Reinforcement Learning

Reinforcement learning (RL) has demonstrated remarkable capabilities in training agents to solve complex tasks autonomously, such as mobile robots, UAVs/UGVs, and game-playing agents). However, scaling RL to master multiple tasks simultaneously (i.e., so-called multi-task RL) remains a significant challenge. Such a multi-task RL capability especially is important for agents to adapt to changes in real-world operational environments. State-of-the-art works show that, training agents with neural networks and shared structures across tasks promises improved generalization in simultaneous multi-task RL. However, they still suffer from task interference and incur high energy consumption due to intensive computation. To address this, we propose MTSpark, a novel methodology that enables energy-efficient simultaneous multi-task RL using spiking neural networks (SNNs) equipped with active dendrites for bio-inspired generalist agents. Specifically, MTSpark enhances a Deep Spiking Q-Network (DSQN) with active dendrites, a dueling structure, and task-specific context signals to dynamically form specialized sub-networks for individual tasks, while exploiting sparse operations for energy-efficient network processing. Experimental results demonstrate that MTSpark achieves higher performance and efficiency compared to state-of-the-art by obtaining high scores across three Atari games (i.e., Pong: -5.4, Breakout: 0.6, and Enduro: 371.2), approaching human-level performance (i.e., Pong: -3, Breakout: 31, Enduro: 368), while incurring similar memory and about 2x lower energy than state-of-the-art. These results show that our MTSpark potentially advances the frontiers toward energy-efficient generalist agents by combining RL and SNNs.

Reinforcement learning agents depend on reward signals whose density is rarely under the designer's control, and when such signals are absent, an agent must generate its own drive to explore. State entropy maximization offers a principled objective for this, but existing methods break down at scale in two ways: the intrinsic reward vanishes once a state has been visited, discouraging revisits to the very gateways that lead onward, and estimating entropy over millions of accumulated observations becomes computationally prohibitive. We address both with Episodic and Lifelong Exploration via Maximum Entropy (ELEMENT), a multiscale intrinsically motivated framework for reward-free exploration that transfers to downstream tasks. ELEMENT couples lifelong entropy maximization with a complementary episodic term acting on a faster timescale. For the episodic term, we derive average episodic state entropy, an intrinsic reward that is the exact minimizer of a tractable upper bound on the reward-decomposition objective; for the lifelong term, we propose a $k$NN graph-based estimator that keeps entropy tractable without forgetting. ELEMENT consistently outperforms state-of-the-art intrinsic reward baselines on state coverage and unsupervised pre-training. Videos, code, and supplementary material: https://sites.google.com/view/element-rl.

Quantum Tiq-Taq-Toe is a well-known benchmark and playground for both quantum computing and machine learning. Despite its popularity, no reinforcement learning (RL) methods have been applied to Quantum Tiq-Taq-Toe. Although there has been some research on Quantum Chess this game is significantly more complex in terms of computation and analysis. Therefore, we study the combination of quantum computing and reinforcement learning in Quantum Tiq-Taq-Toe, which may serve as an accessible testbed for the integration of both fields. Quantum games are challenging to represent classically due to their inherent partial observability and the potential for exponential state complexity. In Quantum Tiq-Taq-Toe, states are observed through Measurement (a 3x3 matrix of state probabilities) and Move History (a 9x9 matrix of entanglement relations), making strategy complex as each move can collapse the quantum state.

The reasoning abilities of large language models (LLMs) have improved with chain-of-thought (CoT) prompting, allowing models to solve complex tasks stepwise. However, training CoT capabilities requires detailed reasoning data, which is often scarce. The self-taught reasoner (STaR) framework addresses this by using reinforcement learning to automatically generate reasoning steps, reducing reliance on human-labeled data. Although STaR and its variants have demonstrated empirical success, a theoretical foundation explaining these improvements is lacking. This work provides a theoretical framework for understanding the effectiveness of reinforcement learning on CoT reasoning and STaR. Our contributions are: (1) criteria for the quality of pre-trained models necessary to initiate effective reasoning improvement; (2) an analysis of policy improvement, showing why LLM reasoning improves iteratively with STaR; (3) conditions for convergence to an optimal reasoning policy; and (4) an examination of STaR's robustness, explaining how it can improve reasoning even when incorporating occasional incorrect steps. We also run RL-STaR on GPT-2, Qwen2.5-0.5B and Phi-3-mini, and the measured return curves follow the ones the analysis predicts. This framework bridges empirical findings with theoretical insights, advancing reinforcement learning approaches for reasoning in LLMs.

Learning from a stream of experience as it arrives, also known as streaming learning, is a core part of natural learning. However, reliable streaming learning has remained a persistent challenge in modern deep reinforcement learning (RL). Instead, most deep RL algorithms learn from old experience by storing past interactions in a buffer. We show that both classical streaming RL, such as Q-learning and actor-critic, when used with deep neural networks, and batch deep RL, such as PPO, SAC, and DQN, when adapted to the streaming setting, often fail to learn. Across 58 Atari games and 50 continuous-control tasks, we find that these methods, in aggregate, perform close to random policies despite extensive task-specific hyperparameter searches. We call this pattern stream barrier. Here, we introduce Stream-X, a shared recipe for streaming deep RL algorithms that combines signal normalization, representation stabilization, and controlled parameter updates. By applying Stream-X to several base streaming RL algorithms, we provide the first family of deep RL algorithms to overcome the stream barrier. Using one prescribed hyperparameter configuration per algorithm across tasks, Stream-X substantially improves aggregate performance, often on par with batch RL algorithms. Beyond these benchmarks, we demonstrate learning with Stream-X algorithms under nonstationarity and resource constraints. Stream-AC, one of the Stream-X algorithms, repeatedly recovers performance across alternating floor-friction regimes in simulation, outperforming the evaluated PPO and SAC baselines. It also learns a heading tracking task on a robot using proprioceptive and visual features from the on-board camera in a naturally changing laboratory environment. Stream-Q learns a Pong game from pixels directly on an ESP32-S3 microcontroller, a device with limited compute and memory.

In the zero-shot policy transfer (ZSPT) setting for contextual Markov decision processes (CMDP), agents train on a fixed, finite set of contexts and must generalize to new ones. Recent work has demonstrated that training on additional states, even if they are irrelevant for solving the current context, can improve generalization to unseen contexts. In this paper, we demonstrate that training on these states can indeed improve generalization, but can come at a cost of reducing the accuracy of the learned value function, which should hurt generalization. We hypothesize and demonstrate that increasing the agent's coverage by training on these additional states while also increasing the accuracy improves generalization even further. Inspired by this, we propose a simple approach Explore-Go that leverages existing pure exploration strategies in a new way: by introducing a pure exploration phase at the start of each training episode. Unlike previous approaches that apply exploration strategies for the purpose of improving generalization, our approach can be combined with both on- and off-policy algorithms. We demonstrate the effectiveness of Explore-Go when combined with several popular algorithms and show an increase in test-time performance across several generalization benchmarks, even partially observable ones. With this, we hope to provide practitioners with a simple modification that can significantly improve the generalization of their agents.

Reach-Avoid-Stay (RAS) tasks are essential in applications where systems must safely reach a target set and remain within it under all bounded disturbances. Existing approaches either struggle to compute the maximal robust RAS set, the set of all states from which the RAS task is achievable, or are limited in handling general dynamic systems. To address these challenges, this paper proposes a two-step deep reinforcement learning framework that jointly learns the maximal robust RAS set and the corresponding control policy. The first step identifies the maximal robust control-invariant set within the target set and derives a policy that ensures the system remains within it. The second step computes the maximal robust reach-avoid (RA) set using this invariant set as the target, and it is proven that this RA set is equivalent to the maximal robust RAS set. Leveraging this result, a switching policy is constructed from the two step-wise policies, which constitutes a valid policy guaranteeing completion of the RAS task. Simulation results demonstrate that the proposed framework (1) computes the exact maximal robust RAS set in the absence of training errors, yielding the least restrictive RAS policy, and (2) identifies the RAS set with high accuracy while outperforming baseline methods on RAS tasks.

We study a structured class of Markov Decision Processes, known as Exo-MDPs, in which the state space is partitioned into exogenous and endogenous components. Exogenous states evolve stochastically, independent of the agent's actions, while endogenous states evolve deterministically based on both state components and actions. Exo-MDPs capture many operations research settings, including inventory control, resource management, and ride-sharing. Our first contribution is structural: we establish a representational equivalence between discrete MDPs, Exo-MDPs, and discrete linear mixture MDPs. Our second contribution is statistical. We characterize the minimax regret of learning in Exo-MDPs when the effective dimension r is small relative to the endogenous state and action spaces. When the exogenous states are unobserved, we prove matching upper and lower regret bounds of order $Θ(Hr \sqrt{K})$ over $K$ episodes of horizon $H$, where $r$ is the effective dimension of the Exo-MDP. When exogenous states are observed, the minimax regret improves to $Θ(H\sqrt{ r K})$, revealing a $Θ(\sqrt{r})$ statistical gap due to observation of the exogenous states. These results show that Exo-MDPs decouple sample complexity from action space and endogenous state space. We validate these insights with experiments on inventory control and resource allocation.

A continual learning agent builds on previous experiences to develop increasingly complex behaviors by adapting to non-stationary and dynamic environments while preserving previously acquired knowledge. However, scaling these systems presents significant challenges, particularly in balancing the preservation of previous policies with the adaptation of new ones to current environments. This balance, known as the stability-plasticity dilemma, is especially pronounced in complex multi-agent domains such as the train scheduling problem, where environmental and agent behaviors are constantly changing, and the search space is vast. In this work, we propose addressing these challenges in the train scheduling problem using curriculum learning. We design a curriculum with adjacent skills that build on each other to improve generalization performance. Introducing a curriculum with distinct tasks introduces non-stationarity, which we address by proposing a new algorithm: Continual Deep Q-Network (DQN) Expansion (CDE). Our approach dynamically generates and adjusts Q-function subspaces to handle environmental changes and task requirements. CDE mitigates catastrophic forgetting through EWC while ensuring high plasticity using adaptive rational activation functions. Experimental results demonstrate significant improvements in learning efficiency and adaptability compared to RL baselines and other adapted methods for continual learning, highlighting the potential of our method in managing the stability-plasticity dilemma in the adaptive train scheduling setting.

Reinforcement learning policies parametrized by deep neural networks have achieved strong performance for continuous control, yet even small input perturbations may lead to unpredictable behavior. This sensitivity limits their use in safety-critical domains, where robustness guarantees are required. Our work addresses this gap between state-of-the-art adversarial training methods and formal verification to train verifiably robust agents. Previous works train networks with individual adversarial perturbations, making them only robust against the specific adversarial attacks used. In contrast, our approach propagates entire perturbed input sets, enclosing all possible adversarial attacks within a single network pass. We leverage this to explicitly penalize the size of the output set (minimizing closed-loop uncertainty) and thereby make the actor robust against all possible attacks. This is realized by the use of set-based policy gradients, where each output within the set has a different gradient, thereby balancing the accuracy and robustness of the network. Doing so, we achieve formal verifiability across different verification frameworks for up to 9 times larger input perturbations compared to standard reinforcement learning and improve certified worst-case performance.

Imagining potential outcomes of actions before execution helps agents make more informed decisions, a prospective thinking ability fundamental to human cognition. However, mainstream model-free Reinforcement Learning (RL) methods lack the ability to proactively envision future scenarios, plan, and guide strategies. These methods typically rely on trial and error to adjust policy functions, aiming to maximize cumulative rewards or long-term value, even if such high-reward decisions place the environment in extremely dangerous states. To address this, we propose the Prospective (ProSpec) RL method, which makes higher-value, lower-risk optimal decisions by imagining future n-stream trajectories. Specifically, ProSpec employs a dynamic model to predict future states (termed "imagined states") based on the current state and a series of sampled actions. Furthermore, we integrate the concept of Model Predictive Control and introduce a cycle consistency constraint that allows the agent to evaluate and select the optimal actions from these trajectories. Moreover, ProSpec employs cycle consistency to mitigate two fundamental issues in RL: augmenting state reversibility to avoid irreversible events (low risk) and augmenting actions to generate numerous virtual trajectories, thereby improving data efficiency. We validated the effectiveness of our method on the DMControl benchmarks, where our approach achieved significant performance improvements. Code will be open-sourced upon acceptance.

Industry is moving toward autonomous, network-connected machines that detect and adapt to changing conditions, including hardware faults. Conventional fault-tolerant design duplicates hardware and reroutes control logic; reinforcement learning (RL) offers a learning-based alternative. This paper presents the first systematic comparison of two RL algorithms -- Proximal Policy Optimization (PPO) and Soft Actor-Critic (SAC) -- for integrating fault tolerance into control. Beyond algorithm choice, we investigate four knowledge-transfer strategies: retaining or discarding model parameters, and retaining or discarding storage contents. Performance is evaluated in two Gymnasium environments: Ant-v5 and FetchReachDense-v3. Results show rapid, fault-specific recovery with clear trade-offs. In Ant-v5, retaining PPO's parameters boosts early returns and remains the safest choice across all faults, while retaining SAC's parameters yields mixed outcomes. SAC's early performance further depends on whether the replay buffer is retained: beneficial when prior experiences match current dynamics, but harmful when they diverge. In FetchReachDense-v3, discarding both PPO's and SAC's parameters was most effective under sensor corruption. Across tasks, both algorithms recover near-normal performance within minutes in low-dimensional settings and within days in high-dimensional settings, highlighting a clear trade-off between adaptation speed and asymptotic performance. These findings demonstrate that RL can deliver robust fault tolerance and offer practical guidelines.

This paper develops a framework for learning in discounted infinite-horizon Markov decision processes (MDPs) with Borel state and action spaces, whose rewards and transitions depend on an unknown parameter.To analyze sampling-based adaptive learning algorithms in this setting, we introduce a canonical probability space that explicitly incorporates sampled parameters into the history of the process. As a performance criterion, we adopt the per-period suboptimality gap used in discounted-MDP regret analysis and specialize it to our parametrized Bayesian setting. Since this quantity captures the remaining loss in future performance from the current period onward, we refer to it as residual regret. We use the expected residual regret to connect discounted-MDP regret analysis with asymptotic discount optimality from adaptive control and the temporal-difference error perspective from reinforcement learning. We then focus on Thompson sampling (TS) in discounted infinite-horizon MDPs. Under assumptions that extend those used in prior work on finite state and action spaces to the Borel setting, we show that the expected residual regret for TS converges to zero exponentially fast. We further show that, under mild conditions ensuring the existence of the relevant limits, the ample-path residual regret converges to zero almost surely and TS achieves complete learning.

Identifying the most suitable variables to represent the state is a fundamental challenge in Reinforcement Learning (RL). These variables must efficiently capture the information necessary for making optimal decisions. In order to address this problem, in this paper, we introduce the Transfer Entropy Redundancy Criterion (TERC), an information-theoretic criterion, which determines if there is entropy transferred from observable state variables to actions during training. We define an algorithm based on TERC that provably excludes variables from the observable state that do not affect the agent's policy during learning. This yields compact state representations that reduce inference time by up to 2.6 times. Our approach is policy-dependent, making it agnostic to the underlying learning algorithm. The efficiency gains we demonstrate arise at retraining and inference time on the reduced state. Our method improves both retraining and inference efficiency. We demonstrate its effectiveness across three distinct algorithm classes, namely tabular Q-learning, Actor-Critic, and Proximal Policy Optimization (PPO), evaluated in a range of environments. Furthermore, to highlight the differences between the proposed methodology and the current state-of-the-art feature selection approaches, we present a series of controlled experiments on synthetic data, before generalizing to real-world decision-making tasks. We also introduce a representation of the problem that compactly captures the transfer of information from observable state variables to actions as Bayesian networks.

Benchmarks are crucial in the development of machine learning algorithms, with available environments significantly influencing reinforcement learning (RL) research. Traditionally, RL environments run on the CPU, which limits their scalability with typical academic compute. However, recent advancements in JAX have enabled the wider use of hardware acceleration, enabling massively parallel RL training pipelines and environments. While this has been successfully applied to single-agent RL, it has not yet been widely adopted for multi-agent scenarios. In this paper, we present JaxMARL, the first open-source, Python-based library that combines GPU-enabled efficiency with support for a large number of commonly used MARL environments and popular baseline algorithms. Our experiments show that, in terms of wall clock time, our JAX-based training pipeline is around 14 times faster than existing approaches, and up to 12500x when multiple training runs are vectorized. This enables efficient and thorough evaluations, potentially alleviating the evaluation crisis in the field. We also introduce and benchmark SMAX, a JAX-based approximate reimplementation of the popular StarCraft Multi-Agent Challenge, which removes the need to run the StarCraft II game engine. This not only enables GPU acceleration, but also provides a more flexible MARL environment, unlocking the potential for self-play, meta-learning, and other future applications in MARL. The code is available at https://github.com/flairox/jaxmarl.

Regularization is a cornerstone of modern reinforcement learning. Regularized policy iteration (RPI) provides a fundamental scheme for solving regularized Markov decision processes (RMDPs), and the widely used soft actor-critic algorithm arises as a special case when the regularizer is Shannon entropy. Despite its empirical success, the theoretical underpinnings of RPI remain unclear. In this paper, we address this gap by proving that RPI is formally equivalent to the standard Newton-Raphson method applied to the Bellman equation smoothed by strongly convex regularizers. This equivalence enables a unified convergence analysis of existing methods and supports the development of accelerated algorithms. We show that RPI enjoys local quadratic convergence; notably, for Shannon entropy, the guarantee is dimension-free. We further study RPI with inexact policy evaluation, establishing its equivalence to an inexact Newton method in which each Newton step is solved via truncated iterations, and derive an asymptotic linear convergence rate of $γ^{M}$, where $M$ denotes the number of operator steps used in policy evaluation. Finally, motivated by higher-order Newton schemes, we propose a new algorithm for RMDPs that achieves third-order local convergence. Numerical experiments corroborate our theory and demonstrate the practical advantages of the proposed algorithm. Overall, our results advance the theoretical understanding of regularization in reinforcement learning and suggest new directions for efficient algorithm design.

Reinforcement learning (RL) performs well in continuous-control tasks, but evolving hidden disturbances create partial observability: the agent must infer decision-relevant latent dynamics from interaction history. This study investigates how observation history, action history, history length, and network structure affect recurrent Twin Delayed Deep Deterministic Policy Gradient (TD3) agents. Three recurrent architectures are evaluated under controlled disturbances with different temporal characteristics. Results show that action history is particularly important when observed responses depend on previous actions, and that processing past and current action-observation information within a unified temporal sequence improves performance compared with using separate branches. We also introduce H-TD3, which reuses recurrent states generated by the actor to initialize the critic, reducing duplicated sequence processing. The architectures are further tested in a simulation-based differential-drive rover motion-regulation task under hidden asymmetric wheel slip. Recurrent architectures retain their advantage under the physically motivated multiplicative wheel-slip model, while policies trained with abstract temporally structured disturbances transfer more effectively to previously unseen wheel-slip dynamics than policies trained without disturbances. These findings provide practical guidance for recurrent RL under partial observability and evolving hidden disturbances.

Hindsight Experience Replay (HER) enhances sample efficiency in goal-conditioned reinforcement learning (RL) by relabelling failed trajectories with goals that were actually achieved. However, HER assumes access to a goal relabelling function and a predicate function that determines whether a goal has been satisfied. These assumptions break down in instruction-following tasks, where goals are expressed in natural language and differ from the state space. We formalize this as the Hindsight Reinforcement Learning problem, which shows the need to jointly learn these functions alongside the RL policy. To address it, we propose ETHER (Emergent Textual Hindsight Experience Replay), an agent that leverages Emergent Communication. ETHER uses a referential game (RG) to train a speaker and a listener to develop a grounded, artificial language describing environment states. It partially aligns this emergent language with instruction language using co-occurrence patterns between task instructions and RL observations. Experiments on BabyAI's PickupDist task show that ETHER's learned RG speaker and listener can function as the goal relabelling and predicate functions of HER, improving sample efficiency despite imperfect language alignment. Our work bridges Emergent Communication and goal-conditioned RL, opening the door to wider applications of HER.

We study a class of reinforcement learning (RL) tasks where the objective of the agent is to accomplish temporally extended goals. In this setting, a common approach is to represent the tasks as deterministic finite automata (DFA) and integrate them into the state-space for RL algorithms. However, while these machines model the reward function, they often overlook the causal knowledge about the environment. To address this limitation, we propose the Temporal-Logic-based Causal Diagram (TL-CD) in RL, which captures the temporal causal relationships between different properties of the environment. We exploit the TL-CD to devise an RL algorithm in which an agent requires significantly less exploration of the environment. To this end, based on a TL-CD and a task DFA, we identify configurations where the agent can determine the expected rewards early during an exploration. Through a series of case studies, we demonstrate the benefits of using TL-CDs, particularly the faster convergence of the algorithm to an optimal policy due to reduced exploration of the environment.

We study formal policy synthesis for continuous-state stochastic systems under linear temporal logic specifications. The product of the system with the automaton of the specification has a hybrid state space with sparse rewards. We introduce a generalized optimal backup order, defined in reverse to a topological order over automaton states, that guides value backups and provably preserves optimality. We further present a model-free actor-critic algorithm whose policy evaluation solves a constrained optimization problem by the augmented Lagrangian method, yielding hyperparameter self-tuning, and prove its optimality and convergence in the tabular case. Since integer encodings of automaton states impose a spurious ordinal relationship on functions learned by one network, we dedicate a value and a policy network to each automaton state (modular learning). The algorithm matches or outperforms PPO, DQN, and A2C on CartPole, and on a Dubins car under a temporal specification the topological order and modular learning raise the success rate from 26.0% to 71.5%.

The 20 Questions (Q20) game is a well known game which encourages deductive reasoning and creativity. In the game, the answerer first thinks of an object such as a famous person or a kind of animal. Then the questioner tries to guess the object by asking 20 questions. In a Q20 game system, the user is considered as the answerer while the system itself acts as the questioner which requires a good strategy of question selection to figure out the correct object and win the game. However, the optimal policy of question selection is hard to be derived due to the complexity and volatility of the game environment. In this paper, we propose a novel policy-based Reinforcement Learning (RL) method, which enables the questioner agent to learn the optimal policy of question selection through continuous interactions with users. To facilitate training, we also propose to use a reward network to estimate the more informative reward. Compared to previous methods, our RL method is robust to noisy answers and does not rely on the Knowledge Base of objects. Experimental results show that our RL method clearly outperforms an entropy-based engineering system and has competitive performance in a noisy-free simulation environment.

Most learning algorithms with formal regret guarantees essentially rely on trying all possible behaviors, which is problematic when some errors cannot be recovered from. Instead, we allow the learning agent to ask for help from a mentor and to transfer knowledge between similar states. We show that this combination enables the agent to learn both safely and effectively. Under standard online learning assumptions, we provide an algorithm whose regret and number of mentor queries are both sublinear in the time horizon for Markov decision processes with irreversible dynamics and infinite state spaces. Our proof involves a sequence of three reductions, making our result more general than a single algorithm. Conceptually, our result may be the first formal proof that it is possible for an agent to obtain high reward while becoming self-sufficient in an unknown, unbounded, and high-stakes environment without resets.

Reinforcement learning (RL) has become a pivotal technology in the post-training phase of large language models (LLMs). Traditional task-collocated RL frameworks suffer from significant scalability bottlenecks, while task-separated RL frameworks face challenges in managing complex dataflows and resolving resource idling. Furthermore, most existing frameworks are tightly coupled with LLM training or inference engines, making them difficult to support custom-designed engines. To address these challenges, we propose AsyncFlow, an asynchronous streaming RL framework tailored for efficient post-training. Specifically, we introduce a distributed data storage and transfer module that provides panoramic data management and fine-grained scheduling capabilities in a fully streamed manner. This architecture inherently enables automated pipeline overlapping among RL tasks and dynamic load-balancing. Moreover, we propose an asynchronous producer-consumer workflow, which is engineered to minimize computational idleness by strategically deferring the parameter update process within staleness thresholds. Finally, the core capabilities of AsyncFlow are architecturally decoupled from underlying training and inference engines and encapsulated by service-oriented user interfaces, offering a modular and customizable user experience. Extensive experiments demonstrate an average throughput of 1.59x compared to the state-of-the-art baseline. The architecture presented in this work provides actionable insights for designing next-generation RL training systems.

This paper introduces a reinforcement learning framework that enables controllable and diverse player behaviors without relying on human gameplay data. Existing approaches often require large-scale player trajectories, train separate models for different player types, or provide no direct mapping between interpretable behavioral parameters and the learned policy, limiting their scalability and controllability. We define player behavior in an N-dimensional continuous space and uniformly sample target behavior vectors from a region that encompasses the subset representing real human styles. During training, each agent receives both its current and target behavior vectors as input, and the reward is based on the normalized reduction in distance between them. This allows the policy to learn how actions influence behavioral statistics, enabling smooth control over attributes such as aggressiveness, mobility, and cooperativeness. A single PPO-based multi-agent policy can reproduce new or unseen play styles without retraining. Experiments conducted in a custom multi-player Unity game show that the proposed framework produces significantly greater behavioral diversity than a win-only baseline and reliably matches specified behavior vectors across diverse targets. The method offers a scalable solution for automated playtesting, game balancing, human-like behavior simulation, and replacing disconnected players in online games.

Generative Flow Networks (GFlowNets) have shown promising potential to generate high-scoring candidates with probability proportional to their rewards. As existing GFlowNets freely explore in state space, they encounter significant convergence challenges when scaling to large state spaces. Addressing this issue, this paper proposes to restrict the exploration of actor. A planner is introduced to partition the entire state space into overlapping partial state spaces. Given their limited size, these partial state spaces allow the actor to efficiently identify subregions with higher rewards. A heuristic strategy is introduced to switch partial regions thus preventing the actor from wasting time exploring fully explored or low-reward partial regions. By iteratively exploring these partial state spaces, the actor learns to converge towards the high-reward subregions within the entire state space. Experiments on several widely used datasets demonstrate that \modelname converges faster than existing works on large state spaces. Furthermore, \modelname not only generates candidates with higher rewards but also significantly improves their diversity.

Credit assignment is a central challenge in reinforcement learning (RL). Classical actor-critic methods address this challenge through fine-grained advantage estimation based on a learned value function. However, learned value models are often avoided in modern large language model (LLM) RL because conventional discriminative critics are difficult to train reliably. We revisit value modeling and argue that this difficulty is partly due to limited expressiveness. In particular, representation complexity theory suggests that value functions can be hard to approximate under the one-shot prediction paradigm used by existing value models, and our scaling experiments show that such critics do not improve reliably with scale. Motivated by this observation, we propose Generative Actor-Critic (GenAC), which replaces one-shot scalar value prediction with a generative critic that performs chain-of-thought reasoning before producing a value estimate. We further introduce In-Context Conditioning, which helps the critic remain calibrated to the current actor throughout training. GenAC improves value approximation, ranking reliability, and out-of-distribution generalization, and these gains translate into stronger downstream RL performance than both value-based and value-free baselines. Overall, our results suggest that stronger value modeling is a promising direction for improving credit assignment in LLM reinforcement learning.

We study Nash equilibrium learning in partially observable Markov games (POMGs), a multi-agent reinforcement learning framework in which agents cannot fully observe the underlying state. Prior work in this setting relies on centralization or information sharing, and suffers from sample and computational complexity that scales exponentially in the number of players. We focus on a subclass of POMGs with independent state transitions, where agents remain coupled through their rewards, and assume that the underlying fully observed Markov game is a Markov potential game. For this class, we present an independent learning algorithm in which players, observing only their own actions and observations and without communication, jointly converge to an approximate Nash equilibrium. Due to partial observability, optimal policies may in general depend on the full action-observation history. Under a filter stability assumption, we show that policies based on finite history windows provide sufficient approximation guarantees. This enables us to approximate the POMG by a surrogate Markov game that is near-potential, leading to quasi-polynomial sample and computational complexity for independent Nash equilibrium learning in the underlying POMG.

Classical reinforcement learning (RL) typically seeks a deterministic policy that maximizes the expected sum of a scalar reward. Yet, modern applications such as language model fine-tuning or scientific discovery demand diversity. Existing remedies such as entropy regularization or diversity bonuses often require fragile trade-offs that sacrifice performance for stochasticity or rely on heuristic metrics that can misalign policy rankings. We argue that diversity is more naturally understood as the rational response to uncertainty in the reward. When the reward function is not perfectly known--as is the case with ambiguous preferences or imperfect reward models--committing to a single action can be sub-optimal. Building on this, we propose a fundamental reformulation of the RL objective by replacing the scalar reward with a distribution over reward functions, and applying a non-linear objective over sets of actions. The result is a framework in which calibrated behavioural diversity emerges naturally, remains controllable through the reward function distribution, and is obtained without sacrificing expected reward. Focusing on the contextual bandit setting as commonly used in large language model (LLM) post-training, we derive a principled gradient estimator for this objective and prove that our formulation naturally generalizes both vanilla policy gradient and more recently developed action-set approaches. We provide didactic experiments which complement our theoretical results, and our large-scale empirical results in LLM reasoning further demonstrate that this framework offers a robust and theoretically grounded alternative for complex RL tasks where the traditional formulation of the problem fails to induce the desired breadth of agent behaviour.