Daily Papers

The success of Large Language Models (LLMs) has sparked interest in various agentic applications. A key hypothesis is that LLMs, leveraging common sense and Chain-of-Thought (CoT) reasoning, can effectively explore and efficiently solve complex domains. However, LLM agents have been found to suffer from sub-optimal exploration and the knowing-doing gap, the inability to effectively act on knowledge present in the model. In this work, we systematically study why LLMs perform sub-optimally in decision-making scenarios. In particular, we closely examine three prevalent failure modes: greediness, frequency bias, and the knowing-doing gap. We propose mitigation of these shortcomings by fine-tuning via Reinforcement Learning (RL) on self-generated CoT rationales. Our experiments across multi-armed bandits, contextual bandits, and Tic-tac-toe, demonstrate that RL fine-tuning enhances the decision-making abilities of LLMs by increasing exploration and narrowing the knowing-doing gap. Finally, we study both classic exploration mechanisms, such as epsilon-greedy, and LLM-specific approaches, such as self-correction and self-consistency, to enable more effective fine-tuning of LLMs for decision-making.

Sample efficiency and exploration remain major challenges in online reinforcement learning (RL). A powerful approach that can be applied to address these issues is the inclusion of offline data, such as prior trajectories from a human expert or a sub-optimal exploration policy. Previous methods have relied on extensive modifications and additional complexity to ensure the effective use of this data. Instead, we ask: can we simply apply existing off-policy methods to leverage offline data when learning online? In this work, we demonstrate that the answer is yes; however, a set of minimal but important changes to existing off-policy RL algorithms are required to achieve reliable performance. We extensively ablate these design choices, demonstrating the key factors that most affect performance, and arrive at a set of recommendations that practitioners can readily apply, whether their data comprise a small number of expert demonstrations or large volumes of sub-optimal trajectories. We see that correct application of these simple recommendations can provide a 2.5times improvement over existing approaches across a diverse set of competitive benchmarks, with no additional computational overhead. We have released our code at https://github.com/ikostrikov/rlpd.

Large language models (LLMs) have been successfully adapted for interactive decision-making tasks like web navigation. While achieving decent performance, previous methods implicitly assume a forward-only execution mode for the model, where they only provide oracle trajectories as in-context examples to teach the model how to reason in the interactive environment. Consequently, the model could not handle more challenging scenarios not covered in the in-context examples, e.g., mistakes, leading to sub-optimal performance. To address this issue, we propose to model the interactive task as state space exploration, where the LLM agent transitions among a pre-defined set of states by performing actions to complete the task. This formulation enables flexible back-tracking, allowing the model to easily recover from errors. We evaluate our proposed LLM Agent with State-Space ExploRation (LASER) on the WebShop task. Experimental results show that our LASER agent significantly outperforms previous methods and closes the gap with human performance on the web navigation task.

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

Recently, large language models (LLMs) have demonstrated impressive performance in Knowledge Graph Question Answering (KGQA) tasks, which aim to find answers based on knowledge graphs (KGs) for natural language questions. Existing LLMs-based KGQA methods typically follow the Graph Retrieval-Augmented Generation (GraphRAG) paradigm, which first retrieves reasoning paths from the large KGs, and then generates the answers based on them. However, these methods emphasize the exploration of new optimal reasoning paths in KGs while ignoring the exploitation of historical reasoning paths, which may lead to sub-optimal reasoning paths. Additionally, the complex semantics contained in questions may lead to the retrieval of inaccurate reasoning paths. To address these issues, this paper proposes a novel and training-free framework for KGQA tasks called Reward-guided Tree Search on Graph (RTSoG). RTSoG decomposes an original question into a series of simpler and well-defined sub-questions to handle the complex semantics. Then, a Self-Critic Monte Carlo Tree Search (SC-MCTS) guided by a reward model is introduced to iteratively retrieve weighted reasoning paths as contextual knowledge. Finally, it stacks the weighted reasoning paths according to their weights to generate the final answers. Extensive experiments on four datasets demonstrate the effectiveness of RTSoG. Notably, it achieves 8.7\% and 7.0\% performance improvement over the state-of-the-art method on the GrailQA and the WebQSP respectively.

Large Language Models (LLMs) have shown remarkable capabilities in natural language tasks requiring complex reasoning, yet their application in agentic, multi-step reasoning within interactive environments remains a difficult challenge. Traditional supervised pre-training on static datasets falls short in enabling autonomous agent capabilities needed to perform complex decision-making in dynamic settings like web navigation. Previous attempts to bridge this ga-through supervised fine-tuning on curated expert demonstrations-often suffer from compounding errors and limited exploration data, resulting in sub-optimal policy outcomes. To overcome these challenges, we propose a framework that combines guided Monte Carlo Tree Search (MCTS) search with a self-critique mechanism and iterative fine-tuning on agent interactions using an off-policy variant of the Direct Preference Optimization (DPO) algorithm. Our method allows LLM agents to learn effectively from both successful and unsuccessful trajectories, thereby improving their generalization in complex, multi-step reasoning tasks. We validate our approach in the WebShop environment-a simulated e-commerce platform where it consistently outperforms behavior cloning and reinforced fine-tuning baseline, and beats average human performance when equipped with the capability to do online search. In real-world booking scenarios, our methodology boosts Llama-3 70B model's zero-shot performance from 18.6% to 81.7% success rate (a 340% relative increase) after a single day of data collection and further to 95.4% with online search. We believe this represents a substantial leap forward in the capabilities of autonomous agents, paving the way for more sophisticated and reliable decision-making in real-world settings.

The rise of large language models (LLMs) has created a significant disparity: industrial research labs with their computational resources, expert teams, and advanced infrastructures, can effectively fine-tune LLMs, while individual developers and small organizations face barriers due to limited resources. In this paper, we aim to bridge this gap by presenting a comprehensive study on supervised fine-tuning of LLMs using instruction-tuning datasets spanning diverse knowledge domains and skills. We focus on small-sized LLMs (3B to 7B parameters) for their cost-efficiency and accessibility. We explore various training configurations and strategies across four open-source pre-trained models. We provide detailed documentation of these configurations, revealing findings that challenge several common training practices, including hyperparameter recommendations from TULU and phased training recommended by Orca. Key insights from our work include: (i) larger batch sizes paired with lower learning rates lead to improved model performance on benchmarks such as MMLU, MTBench, and Open LLM Leaderboard; (ii) early-stage training dynamics, such as lower gradient norms and higher loss values, are strong indicators of better final model performance, enabling early termination of sub-optimal runs and significant computational savings; (iii) through a thorough exploration of hyperparameters like warmup steps and learning rate schedules, we provide guidance for practitioners and find that certain simplifications do not compromise performance; and (iv) we observed no significant difference in performance between phased and stacked training strategies, but stacked training is simpler and more sample efficient. With these findings holding robustly across datasets and models, we hope this study serves as a guide for practitioners fine-tuning small LLMs and promotes a more inclusive environment for LLM research.

Despite the great interest in the bandit problem, designing efficient algorithms for complex models remains challenging, as there is typically no analytical way to quantify uncertainty. In this paper, we propose Multiplier Bootstrap-based Exploration (MBE), a novel exploration strategy that is applicable to any reward model amenable to weighted loss minimization. We prove both instance-dependent and instance-independent rate-optimal regret bounds for MBE in sub-Gaussian multi-armed bandits. With extensive simulation and real data experiments, we show the generality and adaptivity of MBE.

Deep learning algorithms are increasingly employed at the edge. However, edge devices are resource constrained and thus require efficient deployment of deep neural networks. Pruning methods are a key tool for edge deployment as they can improve storage, compute, memory bandwidth, and energy usage. In this paper we propose a novel accurate pruning technique that allows precise control over the output network size. Our method uses an efficient optimal transportation scheme which we make end-to-end differentiable and which automatically tunes the exploration-exploitation behavior of the algorithm to find accurate sparse sub-networks. We show that our method achieves state-of-the-art performance compared to previous pruning methods on 3 different datasets, using 5 different models, across a wide range of pruning ratios, and with two types of sparsity budgets and pruning granularities.

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

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

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al.(2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has mathcal{O}(H^3S^2A/varepsilon^2) sample complexity thus improving the varepsilon-dependence upon existing results, where S is a number of states, A is a number of actions, H is an episode length, and varepsilon is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order mathcal{O}(poly(S,A,H)/varepsilon). Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to mathcal{O}(H^2SA/varepsilon^2), yielding a statistical separation between maximum entropy exploration and reward-free exploration.

Sequential learning with feedback graphs is a natural extension of the multi-armed bandit problem where the problem is equipped with an underlying graph structure that provides additional information - playing an action reveals the losses of all the neighbors of the action. This problem was introduced by mannor2011 and received considerable attention in recent years. It is generally stated in the literature that the minimax regret rate for this problem is of order alpha T, where alpha is the independence number of the graph, and T is the time horizon. However, this is proven only when the number of rounds T is larger than alpha^3, which poses a significant restriction for the usability of this result in large graphs. In this paper, we define a new quantity R^*, called the problem complexity, and prove that the minimax regret is proportional to R^* for any graph and time horizon T. Introducing an intricate exploration strategy, we define the \mainAlgorithm algorithm that achieves the minimax optimal regret bound and becomes the first provably optimal algorithm for this setting, even if T is smaller than alpha^3.

We study the autonomous exploration (AX) problem proposed by Lim & Auer (2012). In this setting, the objective is to discover a set of epsilon-optimal policies reaching a set S_L^{rightarrow} of incrementally L-controllable states. We introduce a novel layered decomposition of the set of incrementally L-controllable states that is based on the iterative application of a state-expansion operator. We leverage these results to design Layered Autonomous Exploration (LAE), a novel algorithm for AX that attains a sample complexity of mathcal{O}(LS^{rightarrow}_{L(1+epsilon)}Gamma_{L(1+epsilon)} A ln^{12}(S^{rightarrow}_{L(1+epsilon)})/epsilon^2), where S^{rightarrow}_{L(1+epsilon)} is the number of states that are incrementally L(1+epsilon)-controllable, A is the number of actions, and Gamma_{L(1+epsilon)} is the branching factor of the transitions over such states. LAE improves over the algorithm of Tarbouriech et al. (2020a) by a factor of L^2 and it is the first algorithm for AX that works in a countably-infinite state space. Moreover, we show that, under a certain identifiability assumption, LAE achieves minimax-optimal sample complexity of mathcal{O}(LS^{rightarrow}_{L}Aln^{12}(S^{rightarrow}_{L})/epsilon^2), outperforming existing algorithms and matching for the first time the lower bound proved by Cai et al. (2022) up to logarithmic factors.

We study the design of sample-efficient algorithms for reinforcement learning in the presence of rich, high-dimensional observations, formalized via the Block MDP problem. Existing algorithms suffer from either 1) computational intractability, 2) strong statistical assumptions that are not necessarily satisfied in practice, or 3) suboptimal sample complexity. We address these issues by providing the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level, with minimal statistical assumptions. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics, a learning objective in which the aim is to predict the learner's own action from the current observation and observations in the (potentially distant) future. MusIK is simple and flexible, and can efficiently take advantage of general-purpose function approximation. Our analysis leverages several new techniques tailored to non-optimistic exploration algorithms, which we anticipate will find broader use.

Learning optimal policies in sparse rewards settings is difficult as the learning agent has little to no feedback on the quality of its actions. In these situations, a good strategy is to focus on exploration, hopefully leading to the discovery of a reward signal to improve on. A learning algorithm capable of dealing with this kind of settings has to be able to (1) explore possible agent behaviors and (2) exploit any possible discovered reward. Efficient exploration algorithms have been proposed that require to define a behavior space, that associates to an agent its resulting behavior in a space that is known to be worth exploring. The need to define this space is a limitation of these algorithms. In this work, we introduce STAX, an algorithm designed to learn a behavior space on-the-fly and to explore it while efficiently optimizing any reward discovered. It does so by separating the exploration and learning of the behavior space from the exploitation of the reward through an alternating two-steps process. In the first step, STAX builds a repertoire of diverse policies while learning a low-dimensional representation of the high-dimensional observations generated during the policies evaluation. In the exploitation step, emitters are used to optimize the performance of the discovered rewarding solutions. Experiments conducted on three different sparse reward environments show that STAX performs comparably to existing baselines while requiring much less prior information about the task as it autonomously builds the behavior space.

Policy search reinforcement learning allows robots to acquire skills by themselves. However, the learning procedure is inherently unsafe as the robot has no a-priori way to predict the consequences of the exploratory actions it takes. Therefore, exploration can lead to collisions with the potential to harm the robot and/or the environment. In this work we address the safety aspect by constraining the exploration to happen in safe-to-explore state spaces. These are formed by decomposing target skills (e.g., grasping) into higher ranked sub-tasks (e.g., collision avoidance, joint limit avoidance) and lower ranked movement tasks (e.g., reaching). Sub-tasks are defined as concurrent controllers (policies) in different operational spaces together with associated Jacobians representing their joint-space mapping. Safety is ensured by only learning policies corresponding to lower ranked sub-tasks in the redundant null space of higher ranked ones. As a side benefit, learning in sub-manifolds of the state-space also facilitates sample efficiency. Reaching skills performed in simulation and grasping skills performed on a real robot validate the usefulness of the proposed approach.

In online reinforcement learning (online RL), balancing exploration and exploitation is crucial for finding an optimal policy in a sample-efficient way. To achieve this, existing sample-efficient online RL algorithms typically consist of three components: estimation, planning, and exploration. However, in order to cope with general function approximators, most of them involve impractical algorithmic components to incentivize exploration, such as optimization within data-dependent level-sets or complicated sampling procedures. To address this challenge, we propose an easy-to-implement RL framework called Maximize to Explore (MEX), which only needs to optimize unconstrainedly a single objective that integrates the estimation and planning components while balancing exploration and exploitation automatically. Theoretically, we prove that MEX achieves a sublinear regret with general function approximations for Markov decision processes (MDP) and is further extendable to two-player zero-sum Markov games (MG). Meanwhile, we adapt deep RL baselines to design practical versions of MEX, in both model-free and model-based manners, which can outperform baselines by a stable margin in various MuJoCo environments with sparse rewards. Compared with existing sample-efficient online RL algorithms with general function approximations, MEX achieves similar sample efficiency while enjoying a lower computational cost and is more compatible with modern deep RL methods.

Exploration bonuses in reinforcement learning guide long-horizon exploration by defining custom intrinsic objectives. Several exploration objectives like count-based bonuses, pseudo-counts, and state-entropy maximization are non-stationary and hence are difficult to optimize for the agent. While this issue is generally known, it is usually omitted and solutions remain under-explored. The key contribution of our work lies in transforming the original non-stationary rewards into stationary rewards through an augmented state representation. For this purpose, we introduce the Stationary Objectives For Exploration (SOFE) framework. SOFE requires identifying sufficient statistics for different exploration bonuses and finding an efficient encoding of these statistics to use as input to a deep network. SOFE is based on proposing state augmentations that expand the state space but hold the promise of simplifying the optimization of the agent's objective. We show that SOFE improves the performance of several exploration objectives, including count-based bonuses, pseudo-counts, and state-entropy maximization. Moreover, SOFE outperforms prior methods that attempt to stabilize the optimization of intrinsic objectives. We demonstrate the efficacy of SOFE in hard-exploration problems, including sparse-reward tasks, pixel-based observations, 3D navigation, and procedurally generated environments.

Model-based reinforcement learning is a powerful tool, but collecting data to fit an accurate model of the system can be costly. Exploring an unknown environment in a sample-efficient manner is hence of great importance. However, the complexity of dynamics and the computational limitations of real systems make this task challenging. In this work, we introduce FLEX, an exploration algorithm for nonlinear dynamics based on optimal experimental design. Our policy maximizes the information of the next step and results in an adaptive exploration algorithm, compatible with generic parametric learning models and requiring minimal resources. We test our method on a number of nonlinear environments covering different settings, including time-varying dynamics. Keeping in mind that exploration is intended to serve an exploitation objective, we also test our algorithm on downstream model-based classical control tasks and compare it to other state-of-the-art model-based and model-free approaches. The performance achieved by FLEX is competitive and its computational cost is low.

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.

In this paper, we present empirical evidence of skills and directed exploration emerging from a simple RL algorithm long before any successful trials are observed. For example, in a manipulation task, the agent is given a single observation of the goal state and learns skills, first for moving its end-effector, then for pushing the block, and finally for picking up and placing the block. These skills emerge before the agent has ever successfully placed the block at the goal location and without the aid of any reward functions, demonstrations, or manually-specified distance metrics. Once the agent has learned to reach the goal state reliably, exploration is reduced. Implementing our method involves a simple modification of prior work and does not require density estimates, ensembles, or any additional hyperparameters. Intuitively, the proposed method seems like it should be terrible at exploration, and we lack a clear theoretical understanding of why it works so effectively, though our experiments provide some hints.

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm--using only the number of iterations as feedback--can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

Go-Explore is a powerful family of algorithms designed to solve hard-exploration problems, built on the principle of archiving discovered states, and iteratively returning to and exploring from the most promising states. This approach has led to superhuman performance across a wide variety of challenging problems including Atari games and robotic control, but requires manually designing heuristics to guide exploration, which is time-consuming and infeasible in general. To resolve this, we propose Intelligent Go-Explore (IGE) which greatly extends the scope of the original Go-Explore by replacing these heuristics with the intelligence and internalized human notions of interestingness captured by giant foundation models (FMs). This provides IGE with a human-like ability to instinctively identify how interesting or promising any new state is (e.g. discovering new objects, locations, or behaviors), even in complex environments where heuristics are hard to define. Moreover, IGE offers the exciting and previously impossible opportunity to recognize and capitalize on serendipitous discoveries that cannot be predicted ahead of time. We evaluate IGE on a range of language-based tasks that require search and exploration. In Game of 24, a multistep mathematical reasoning problem, IGE reaches 100% success rate 70.8% faster than the best classic graph search baseline. Next, in BabyAI-Text, a challenging partially observable gridworld, IGE exceeds the previous SOTA with orders of magnitude fewer online samples. Finally, in TextWorld, we show the unique ability of IGE to succeed in settings requiring long-horizon exploration where prior SOTA FM agents like Reflexion completely fail. Overall, IGE combines the tremendous strengths of FMs and the powerful Go-Explore algorithm, opening up a new frontier of research into creating more generally capable agents with impressive exploration capabilities.

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

A grand challenge in reinforcement learning is intelligent exploration, especially when rewards are sparse or deceptive. Two Atari games serve as benchmarks for such hard-exploration domains: Montezuma's Revenge and Pitfall. On both games, current RL algorithms perform poorly, even those with intrinsic motivation, which is the dominant method to improve performance on hard-exploration domains. To address this shortfall, we introduce a new algorithm called Go-Explore. It exploits the following principles: (1) remember previously visited states, (2) first return to a promising state (without exploration), then explore from it, and (3) solve simulated environments through any available means (including by introducing determinism), then robustify via imitation learning. The combined effect of these principles is a dramatic performance improvement on hard-exploration problems. On Montezuma's Revenge, Go-Explore scores a mean of over 43k points, almost 4 times the previous state of the art. Go-Explore can also harness human-provided domain knowledge and, when augmented with it, scores a mean of over 650k points on Montezuma's Revenge. Its max performance of nearly 18 million surpasses the human world record, meeting even the strictest definition of "superhuman" performance. On Pitfall, Go-Explore with domain knowledge is the first algorithm to score above zero. Its mean score of almost 60k points exceeds expert human performance. Because Go-Explore produces high-performing demonstrations automatically and cheaply, it also outperforms imitation learning work where humans provide solution demonstrations. Go-Explore opens up many new research directions into improving it and weaving its insights into current RL algorithms. It may also enable progress on previously unsolvable hard-exploration problems in many domains, especially those that harness a simulator during training (e.g. robotics).

There is a strong link between the general concept of intelligence and the ability to collect and use information. The theory of Bayes-adaptive exploration offers an attractive optimality framework for training machines to perform complex information gathering tasks. However, the computational complexity of the resulting optimal control problem has limited the diffusion of the theory to mainstream deep AI research. In this paper we exploit the inherent mathematical structure of Bayes-adaptive problems in order to dramatically simplify the problem by making the reward structure denser while simultaneously decoupling the learning of exploitation and exploration policies. The key to this simplification comes from the novel concept of cross-value (i.e. the value of being in an environment while acting optimally according to another), which we use to quantify the value of currently available information. This results in a new denser reward structure that "cashes in" all future rewards that can be predicted from the current information state. In a set of experiments we show that the approach makes it possible to learn challenging information gathering tasks without the use of shaping and heuristic bonuses in situations where the standard RL algorithms fail.

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.

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

In deep reinforcement learning (RL) research, there has been a concerted effort to design more efficient and productive exploration methods while solving sparse-reward problems. These exploration methods often share common principles (e.g., improving diversity) and implementation details (e.g., intrinsic reward). Prior work found that non-stationary Markov decision processes (MDPs) require exploration to efficiently adapt to changes in the environment with online transfer learning. However, the relationship between specific exploration characteristics and effective transfer learning in deep RL has not been characterized. In this work, we seek to understand the relationships between salient exploration characteristics and improved performance and efficiency in transfer learning. We test eleven popular exploration algorithms on a variety of transfer types -- or ``novelties'' -- to identify the characteristics that positively affect online transfer learning. Our analysis shows that some characteristics correlate with improved performance and efficiency across a wide range of transfer tasks, while others only improve transfer performance with respect to specific environment changes. From our analysis, make recommendations about which exploration algorithm characteristics are best suited to specific transfer situations.

Efficiently tackling combinatorial reasoning problems, particularly the notorious NP-hard tasks, remains a significant challenge for AI research. Recent efforts have sought to enhance planning by incorporating hierarchical high-level search strategies, known as subgoal methods. While promising, their performance against traditional low-level planners is inconsistent, raising questions about their application contexts. In this study, we conduct an in-depth exploration of subgoal-planning methods for combinatorial reasoning. We identify the attributes pivotal for leveraging the advantages of high-level search: hard-to-learn value functions, complex action spaces, presence of dead ends in the environment, or using data collected from diverse experts. We propose a consistent evaluation methodology to achieve meaningful comparisons between methods and reevaluate the state-of-the-art algorithms.

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.

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

The Multi-armed bandit offer the advantage to learn and exploit the already learnt knowledge at the same time. This capability allows this approach to be applied in different domains, going from clinical trials where the goal is investigating the effects of different experimental treatments while minimizing patient losses, to adaptive routing where the goal is to minimize the delays in a network. This article provides a review of the recent results on applying bandit to real-life scenario and summarize the state of the art for each of these fields. Different techniques has been proposed to solve this problem setting, like epsilon-greedy, Upper confident bound (UCB) and Thompson Sampling (TS). We are showing here how this algorithms were adapted to solve the different problems of exploration exploitation.

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

We investigate the online bandit learning of the monotone multi-linear DR-submodular functions, designing the algorithm BanditMLSM that attains O(T^{2/3}log T) of (1-1/e)-regret. Then we reduce submodular bandit with partition matroid constraint and bandit sequential monotone maximization to the online bandit learning of the monotone multi-linear DR-submodular functions, attaining O(T^{2/3}log T) of (1-1/e)-regret in both problems, which improve the existing results. To the best of our knowledge, we are the first to give a sublinear regret algorithm for the submodular bandit with partition matroid constraint. A special case of this problem is studied by Streeter et al.(2009). They prove a O(T^{4/5}) (1-1/e)-regret upper bound. For the bandit sequential submodular maximization, the existing work proves an O(T^{2/3}) regret with a suboptimal 1/2 approximation ratio (Niazadeh et al. 2021).

Reward-based optimization algorithms require both exploration, to find rewards, and exploitation, to maximize performance. The need for efficient exploration is even more significant in sparse reward settings, in which performance feedback is given sparingly, thus rendering it unsuitable for guiding the search process. In this work, we introduce the SparsE Reward Exploration via Novelty and Emitters (SERENE) algorithm, capable of efficiently exploring a search space, as well as optimizing rewards found in potentially disparate areas. Contrary to existing emitters-based approaches, SERENE separates the search space exploration and reward exploitation into two alternating processes. The first process performs exploration through Novelty Search, a divergent search algorithm. The second one exploits discovered reward areas through emitters, i.e. local instances of population-based optimization algorithms. A meta-scheduler allocates a global computational budget by alternating between the two processes, ensuring the discovery and efficient exploitation of disjoint reward areas. SERENE returns both a collection of diverse solutions covering the search space and a collection of high-performing solutions for each distinct reward area. We evaluate SERENE on various sparse reward environments and show it compares favorably to existing baselines.

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

We present a representation-driven framework for reinforcement learning. By representing policies as estimates of their expected values, we leverage techniques from contextual bandits to guide exploration and exploitation. Particularly, embedding a policy network into a linear feature space allows us to reframe the exploration-exploitation problem as a representation-exploitation problem, where good policy representations enable optimal exploration. We demonstrate the effectiveness of this framework through its application to evolutionary and policy gradient-based approaches, leading to significantly improved performance compared to traditional methods. Our framework provides a new perspective on reinforcement learning, highlighting the importance of policy representation in determining optimal exploration-exploitation strategies.

Reinforcement learning (RL) agents improve through trial-and-error, but when reward is sparse and the agent cannot discover successful action sequences, learning stagnates. This has been a notable problem in training deep RL agents to perform web-based tasks, such as booking flights or replying to emails, where a single mistake can ruin the entire sequence of actions. A common remedy is to "warm-start" the agent by pre-training it to mimic expert demonstrations, but this is prone to overfitting. Instead, we propose to constrain exploration using demonstrations. From each demonstration, we induce high-level "workflows" which constrain the allowable actions at each time step to be similar to those in the demonstration (e.g., "Step 1: click on a textbox; Step 2: enter some text"). Our exploration policy then learns to identify successful workflows and samples actions that satisfy these workflows. Workflows prune out bad exploration directions and accelerate the agent's ability to discover rewards. We use our approach to train a novel neural policy designed to handle the semi-structured nature of websites, and evaluate on a suite of web tasks, including the recent World of Bits benchmark. We achieve new state-of-the-art results, and show that workflow-guided exploration improves sample efficiency over behavioral cloning by more than 100x.

We advance the study of incentivized bandit exploration, in which arm choices are viewed as recommendations and are required to be Bayesian incentive compatible. Recent work has shown under certain independence assumptions that after collecting enough initial samples, the popular Thompson sampling algorithm becomes incentive compatible. We give an analog of this result for linear bandits, where the independence of the prior is replaced by a natural convexity condition. This opens up the possibility of efficient and regret-optimal incentivized exploration in high-dimensional action spaces. In the semibandit model, we also improve the sample complexity for the pre-Thompson sampling phase of initial data collection.

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

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

Large Language Models (LLMs) can self-improve through reinforcement learning, where they generate trajectories to explore and discover better solutions. However, this exploration process is computationally expensive, often forcing current methods to assign limited exploration budgets to each task. This uniform allocation creates problematic edge cases: easy tasks consistently succeed while difficult tasks consistently fail, both producing zero gradients during training updates for the widely used Group Relative Policy Optimization (GRPO). We address this problem from the lens of exploration budget allocation. Viewing each task's exploration as an "item" with a distinct "value" and "cost", we establish a connection to the classical knapsack problem. This formulation allows us to derive an optimal assignment rule that adaptively distributes resources based on the model's current learning status. When applied to GRPO, our method increases the effective ratio of non-zero policy gradients by 20-40% during training. Acting as a computational "free lunch", our approach could reallocate exploration budgets from tasks where learning is saturated to those where it is most impactful. This enables significantly larger budgets (e.g., 93 rollouts) for especially challenging problems, which would be computationally prohibitive under a uniform allocation. These improvements translate to meaningful gains on mathematical reasoning benchmarks, with average improvements of 2-4 points and peak gains of 9 points on specific tasks. Notably, achieving comparable performance with traditional homogeneous allocation would require about 2x the computational resources.

Unsupervised goal-conditioned reinforcement learning (GCRL) is a promising paradigm for developing diverse robotic skills without external supervision. However, existing unsupervised GCRL methods often struggle to cover a wide range of states in complex environments due to their limited exploration and sparse or noisy rewards for GCRL. To overcome these challenges, we propose a novel unsupervised GCRL method that leverages TemporaL Distance-aware Representations (TLDR). TLDR selects faraway goals to initiate exploration and computes intrinsic exploration rewards and goal-reaching rewards, based on temporal distance. Specifically, our exploration policy seeks states with large temporal distances (i.e. covering a large state space), while the goal-conditioned policy learns to minimize the temporal distance to the goal (i.e. reaching the goal). Our experimental results in six simulated robotic locomotion environments demonstrate that our method significantly outperforms previous unsupervised GCRL methods in achieving a wide variety of states.

In this paper, we introduce Latent Go-Explore (LGE), a simple and general approach based on the Go-Explore paradigm for exploration in reinforcement learning (RL). Go-Explore was initially introduced with a strong domain knowledge constraint for partitioning the state space into cells. However, in most real-world scenarios, drawing domain knowledge from raw observations is complex and tedious. If the cell partitioning is not informative enough, Go-Explore can completely fail to explore the environment. We argue that the Go-Explore approach can be generalized to any environment without domain knowledge and without cells by exploiting a learned latent representation. Thus, we show that LGE can be flexibly combined with any strategy for learning a latent representation. Our results indicate that LGE, although simpler than Go-Explore, is more robust and outperforms state-of-the-art algorithms in terms of pure exploration on multiple hard-exploration environments including Montezuma's Revenge. The LGE implementation is available as open-source at https://github.com/qgallouedec/lge.

We describe a robotic learning system for autonomous exploration and navigation in diverse, open-world environments. At the core of our method is a learned latent variable model of distances and actions, along with a non-parametric topological memory of images. We use an information bottleneck to regularize the learned policy, giving us (i) a compact visual representation of goals, (ii) improved generalization capabilities, and (iii) a mechanism for sampling feasible goals for exploration. Trained on a large offline dataset of prior experience, the model acquires a representation of visual goals that is robust to task-irrelevant distractors. We demonstrate our method on a mobile ground robot in open-world exploration scenarios. Given an image of a goal that is up to 80 meters away, our method leverages its representation to explore and discover the goal in under 20 minutes, even amidst previously-unseen obstacles and weather conditions. Please check out the project website for videos of our experiments and information about the real-world dataset used at https://sites.google.com/view/recon-robot.

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.

In this paper, we introduce the Preselection Bandit problem, in which the learner preselects a subset of arms (choice alternatives) for a user, which then chooses the final arm from this subset. The learner is not aware of the user's preferences, but can learn them from observed choices. In our concrete setting, we allow these choices to be stochastic and model the user's actions by means of the Plackett-Luce model. The learner's main task is to preselect subsets that eventually lead to highly preferred choices. To formalize this goal, we introduce a reasonable notion of regret and derive lower bounds on the expected regret. Moreover, we propose algorithms for which the upper bound on expected regret matches the lower bound up to a logarithmic term of the time horizon.

Exploration is a key problem in reinforcement learning, since agents can only learn from data they acquire in the environment. With that in mind, maintaining a population of agents is an attractive method, as it allows data be collected with a diverse set of behaviors. This behavioral diversity is often boosted via multi-objective loss functions. However, those approaches typically leverage mean field updates based on pairwise distances, which makes them susceptible to cycling behaviors and increased redundancy. In addition, explicitly boosting diversity often has a detrimental impact on optimizing already fruitful behaviors for rewards. As such, the reward-diversity trade off typically relies on heuristics. Finally, such methods require behavioral representations, often handcrafted and domain specific. In this paper, we introduce an approach to optimize all members of a population simultaneously. Rather than using pairwise distance, we measure the volume of the entire population in a behavioral manifold, defined by task-agnostic behavioral embeddings. In addition, our algorithm Diversity via Determinants (DvD), adapts the degree of diversity during training using online learning techniques. We introduce both evolutionary and gradient-based instantiations of DvD and show they effectively improve exploration without reducing performance when better exploration is not required.

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.

Multitask Reinforcement Learning (MTRL) approaches have gained increasing attention for its wide applications in many important Reinforcement Learning (RL) tasks. However, while recent advancements in MTRL theory have focused on the improved statistical efficiency by assuming a shared structure across tasks, exploration--a crucial aspect of RL--has been largely overlooked. This paper addresses this gap by showing that when an agent is trained on a sufficiently diverse set of tasks, a generic policy-sharing algorithm with myopic exploration design like epsilon-greedy that are inefficient in general can be sample-efficient for MTRL. To the best of our knowledge, this is the first theoretical demonstration of the "exploration benefits" of MTRL. It may also shed light on the enigmatic success of the wide applications of myopic exploration in practice. To validate the role of diversity, we conduct experiments on synthetic robotic control environments, where the diverse task set aligns with the task selection by automatic curriculum learning, which is empirically shown to improve sample-efficiency.

Beyond high-fidelity image synthesis, diffusion models have recently exhibited promising results in dense visual perception tasks. However, most existing work treats diffusion models as a standalone component for perception tasks, employing them either solely for off-the-shelf data augmentation or as mere feature extractors. In contrast to these isolated and thus sub-optimal efforts, we introduce a unified, versatile, diffusion-based framework, Diff-2-in-1, that can simultaneously handle both multi-modal data generation and dense visual perception, through a unique exploitation of the diffusion-denoising process. Within this framework, we further enhance discriminative visual perception via multi-modal generation, by utilizing the denoising network to create multi-modal data that mirror the distribution of the original training set. Importantly, Diff-2-in-1 optimizes the utilization of the created diverse and faithful data by leveraging a novel self-improving learning mechanism. Comprehensive experimental evaluations validate the effectiveness of our framework, showcasing consistent performance improvements across various discriminative backbones and high-quality multi-modal data generation characterized by both realism and usefulness.

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

We study linear contextual bandits in the misspecified setting, where the expected reward function can be approximated by a linear function class up to a bounded misspecification level zeta>0. We propose an algorithm based on a novel data selection scheme, which only selects the contextual vectors with large uncertainty for online regression. We show that, when the misspecification level zeta is dominated by tilde O (Delta / d) with Delta being the minimal sub-optimality gap and d being the dimension of the contextual vectors, our algorithm enjoys the same gap-dependent regret bound tilde O (d^2/Delta) as in the well-specified setting up to logarithmic factors. In addition, we show that an existing algorithm SupLinUCB (Chu et al., 2011) can also achieve a gap-dependent constant regret bound without the knowledge of sub-optimality gap Delta. Together with a lower bound adapted from Lattimore et al. (2020), our result suggests an interplay between misspecification level and the sub-optimality gap: (1) the linear contextual bandit model is efficiently learnable when zeta leq tilde O(Delta / d); and (2) it is not efficiently learnable when zeta geq tilde Omega({Delta} / {d}). Experiments on both synthetic and real-world datasets corroborate our theoretical results.

Recent flow matching models for text-to-image generation have achieved remarkable quality, yet their integration with reinforcement learning for human preference alignment remains suboptimal, hindering fine-grained reward-based optimization. We observe that the key impediment to effective GRPO training of flow models is the temporal uniformity assumption in existing approaches: sparse terminal rewards with uniform credit assignment fail to capture the varying criticality of decisions across generation timesteps, resulting in inefficient exploration and suboptimal convergence. To remedy this shortcoming, we introduce TempFlow-GRPO (Temporal Flow GRPO), a principled GRPO framework that captures and exploits the temporal structure inherent in flow-based generation. TempFlow-GRPO introduces two key innovations: (i) a trajectory branching mechanism that provides process rewards by concentrating stochasticity at designated branching points, enabling precise credit assignment without requiring specialized intermediate reward models; and (ii) a noise-aware weighting scheme that modulates policy optimization according to the intrinsic exploration potential of each timestep, prioritizing learning during high-impact early stages while ensuring stable refinement in later phases. These innovations endow the model with temporally-aware optimization that respects the underlying generative dynamics, leading to state-of-the-art performance in human preference alignment and standard text-to-image benchmarks.

In the Reinforcement Learning (RL) framework, the learning is guided through a reward signal. This means that in situations of sparse rewards the agent has to focus on exploration, in order to discover which action, or set of actions leads to the reward. RL agents usually struggle with this. Exploration is the focus of Quality-Diversity (QD) methods. In this thesis, we approach the problem of sparse rewards with these algorithms, and in particular with Novelty Search (NS). This is a method that only focuses on the diversity of the possible policies behaviors. The first part of the thesis focuses on learning a representation of the space in which the diversity of the policies is evaluated. In this regard, we propose the TAXONS algorithm, a method that learns a low-dimensional representation of the search space through an AutoEncoder. While effective, TAXONS still requires information on when to capture the observation used to learn said space. For this, we study multiple ways, and in particular the signature transform, to encode information about the whole trajectory of observations. The thesis continues with the introduction of the SERENE algorithm, a method that can efficiently focus on the interesting parts of the search space. This method separates the exploration of the search space from the exploitation of the reward through a two-alternating-steps approach. The exploration is performed through NS. Any discovered reward is then locally exploited through emitters. The third and final contribution combines TAXONS and SERENE into a single approach: STAX. Throughout this thesis, we introduce methods that lower the amount of prior information needed in sparse rewards settings. These contributions are a promising step towards the development of methods that can autonomously explore and find high-performance policies in a variety of sparse rewards settings.

Selecting exploratory actions that generate a rich stream of experience for better learning is a fundamental challenge in reinforcement learning (RL). An approach to tackle this problem consists in selecting actions according to specific policies for an extended period of time, also known as options. A recent line of work to derive such exploratory options builds upon the eigenfunctions of the graph Laplacian. Importantly, until now these methods have been mostly limited to tabular domains where (1) the graph Laplacian matrix was either given or could be fully estimated, (2) performing eigendecomposition on this matrix was computationally tractable, and (3) value functions could be learned exactly. Additionally, these methods required a separate option discovery phase. These assumptions are fundamentally not scalable. In this paper we address these limitations and show how recent results for directly approximating the eigenfunctions of the Laplacian can be leveraged to truly scale up options-based exploration. To do so, we introduce a fully online deep RL algorithm for discovering Laplacian-based options and evaluate our approach on a variety of pixel-based tasks. We compare to several state-of-the-art exploration methods and show that our approach is effective, general, and especially promising in non-stationary settings.

We study reinforcement learning with linear function approximation and adversarially changing cost functions, a setup that has mostly been considered under simplifying assumptions such as full information feedback or exploratory conditions.We present a computationally efficient policy optimization algorithm for the challenging general setting of unknown dynamics and bandit feedback, featuring a combination of mirror-descent and least squares policy evaluation in an auxiliary MDP used to compute exploration bonuses.Our algorithm obtains an widetilde O(K^{6/7}) regret bound, improving significantly over previous state-of-the-art of widetilde O (K^{14/15}) in this setting. In addition, we present a version of the same algorithm under the assumption a simulator of the environment is available to the learner (but otherwise no exploratory assumptions are made), and prove it obtains state-of-the-art regret of widetilde O (K^{2/3}).

In this paper, we propose an enhanced approach for Rapid Exploration and eXploitation for AI Agents called REX. Existing AutoGPT-style techniques have inherent limitations, such as a heavy reliance on precise descriptions for decision-making, and the lack of a systematic approach to leverage try-and-fail procedures akin to traditional Reinforcement Learning (RL). REX introduces an additional layer of rewards and integrates concepts similar to Upper Confidence Bound (UCB) scores, leading to more robust and efficient AI agent performance. This approach has the advantage of enabling the utilization of offline behaviors from logs and allowing seamless integration with existing foundation models while it does not require any model fine-tuning. Through comparative analysis with existing methods such as Chain-of-Thoughts(CoT) and Reasoning viA Planning(RAP), REX-based methods demonstrate comparable performance and, in certain cases, even surpass the results achieved by these existing techniques. Notably, REX-based methods exhibit remarkable reductions in execution time, enhancing their practical applicability across a diverse set of scenarios.

Reinforcement learning usually uses the feedback rewards of environmental to train agents. But the rewards in the actual environment are sparse, and even some environments will not rewards. Most of the current methods are difficult to get good performance in sparse reward or non-reward environments. Although using shaped rewards is effective when solving sparse reward tasks, it is limited to specific problems and learning is also susceptible to local optima. We propose a model-free method that does not rely on environmental rewards to solve the problem of sparse rewards in the general environment. Our method use the minimum number of transitions between states as the distance to replace the rewards of environmental, and proposes a goal-distance gradient to achieve policy improvement. We also introduce a bridge point planning method based on the characteristics of our method to improve exploration efficiency, thereby solving more complex tasks. Experiments show that our method performs better on sparse reward and local optimal problems in complex environments than previous work.

Combinatorial Optimization underpins many real-world applications and yet, designing performant algorithms to solve these complex, typically NP-hard, problems remains a significant research challenge. Reinforcement Learning (RL) provides a versatile framework for designing heuristics across a broad spectrum of problem domains. However, despite notable progress, RL has not yet supplanted industrial solvers as the go-to solution. Current approaches emphasize pre-training heuristics that construct solutions but often rely on search procedures with limited variance, such as stochastically sampling numerous solutions from a single policy or employing computationally expensive fine-tuning of the policy on individual problem instances. Building on the intuition that performant search at inference time should be anticipated during pre-training, we propose COMPASS, a novel RL approach that parameterizes a distribution of diverse and specialized policies conditioned on a continuous latent space. We evaluate COMPASS across three canonical problems - Travelling Salesman, Capacitated Vehicle Routing, and Job-Shop Scheduling - and demonstrate that our search strategy (i) outperforms state-of-the-art approaches on 11 standard benchmarking tasks and (ii) generalizes better, surpassing all other approaches on a set of 18 procedurally transformed instance distributions.

Inverse reinforcement learning (IRL) denotes a powerful family of algorithms for recovering a reward function justifying the behavior demonstrated by an expert agent. A well-known limitation of IRL is the ambiguity in the choice of the reward function, due to the existence of multiple rewards that explain the observed behavior. This limitation has been recently circumvented by formulating IRL as the problem of estimating the feasible reward set, i.e., the region of the rewards compatible with the expert's behavior. In this paper, we make a step towards closing the theory gap of IRL in the case of finite-horizon problems with a generative model. We start by formally introducing the problem of estimating the feasible reward set, the corresponding PAC requirement, and discussing the properties of particular classes of rewards. Then, we provide the first minimax lower bound on the sample complexity for the problem of estimating the feasible reward set of order {Omega}Bigl( H^3SA{epsilon^2} bigl( log bigl(1{delta}bigl) + S bigl)Bigl), being S and A the number of states and actions respectively, H the horizon, epsilon the desired accuracy, and delta the confidence. We analyze the sample complexity of a uniform sampling strategy (US-IRL), proving a matching upper bound up to logarithmic factors. Finally, we outline several open questions in IRL and propose future research directions.

In risk-averse reinforcement learning (RL), the goal is to optimize some risk measure of the returns. A risk measure often focuses on the worst returns out of the agent's experience. As a result, standard methods for risk-averse RL often ignore high-return strategies. We prove that under certain conditions this inevitably leads to a local-optimum barrier, and propose a soft risk mechanism to bypass it. We also devise a novel Cross Entropy module for risk sampling, which (1) preserves risk aversion despite the soft risk; (2) independently improves sample efficiency. By separating the risk aversion of the sampler and the optimizer, we can sample episodes with poor conditions, yet optimize with respect to successful strategies. We combine these two concepts in CeSoR - Cross-entropy Soft-Risk optimization algorithm - which can be applied on top of any risk-averse policy gradient (PG) method. We demonstrate improved risk aversion in maze navigation, autonomous driving, and resource allocation benchmarks, including in scenarios where standard risk-averse PG completely fails.

We study reinforcement learning for global decision-making in the presence of many local agents, where the global decision-maker makes decisions affecting all local agents, and the objective is to learn a policy that maximizes the rewards of both the global and the local agents. Such problems find many applications, e.g. demand response, EV charging, queueing, etc. In this setting, scalability has been a long-standing challenge due to the size of the state/action space which can be exponential in the number of agents. This work proposes the SUB-SAMPLE-Q algorithm where the global agent subsamples kleq n local agents to compute an optimal policy in time that is only exponential in k, providing an exponential speedup from standard methods that are exponential in n. We show that the learned policy converges to the optimal policy in the order of O(1/k+epsilon_{k,m}) as the number of sub-sampled agents k increases, where epsilon_{k,m} is the Bellman noise. We also conduct numerical simulations in a demand-response setting and a queueing setting.

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

We study multi-agent reinforcement learning (MARL) for the general-sum Markov Games (MGs) under the general function approximation. In order to find the minimum assumption for sample-efficient learning, we introduce a novel complexity measure called the Multi-Agent Decoupling Coefficient (MADC) for general-sum MGs. Using this measure, we propose the first unified algorithmic framework that ensures sample efficiency in learning Nash Equilibrium, Coarse Correlated Equilibrium, and Correlated Equilibrium for both model-based and model-free MARL problems with low MADC. We also show that our algorithm provides comparable sublinear regret to the existing works. Moreover, our algorithm combines an equilibrium-solving oracle with a single objective optimization subprocedure that solves for the regularized payoff of each deterministic joint policy, which avoids solving constrained optimization problems within data-dependent constraints (Jin et al. 2020; Wang et al. 2023) or executing sampling procedures with complex multi-objective optimization problems (Foster et al. 2023), thus being more amenable to empirical implementation.

In light of the burgeoning success of reinforcement learning (RL) in diverse real-world applications, considerable focus has been directed towards ensuring RL policies are robust to adversarial attacks during test time. Current approaches largely revolve around solving a minimax problem to prepare for potential worst-case scenarios. While effective against strong attacks, these methods often compromise performance in the absence of attacks or the presence of only weak attacks. To address this, we study policy robustness under the well-accepted state-adversarial attack model, extending our focus beyond only worst-case attacks. We first formalize this task at test time as a regret minimization problem and establish its intrinsic hardness in achieving sublinear regret when the baseline policy is from a general continuous policy class, Pi. This finding prompts us to refine the baseline policy class Pi prior to test time, aiming for efficient adaptation within a finite policy class Pi, which can resort to an adversarial bandit subroutine. In light of the importance of a small, finite Pi, we propose a novel training-time algorithm to iteratively discover non-dominated policies, forming a near-optimal and minimal Pi, thereby ensuring both robustness and test-time efficiency. Empirical validation on the Mujoco corroborates the superiority of our approach in terms of natural and robust performance, as well as adaptability to various attack scenarios.

In a recent work, Laforgue et al. introduce the model of last switch dependent (LSD) bandits, in an attempt to capture nonstationary phenomena induced by the interaction between the player and the environment. Examples include satiation, where consecutive plays of the same action lead to decreased performance, or deprivation, where the payoff of an action increases after an interval of inactivity. In this work, we take a step towards understanding the approximability of planning LSD bandits, namely, the (NP-hard) problem of computing an optimal arm-pulling strategy under complete knowledge of the model. In particular, we design the first efficient constant approximation algorithm for the problem and show that, under a natural monotonicity assumption on the payoffs, its approximation guarantee (almost) matches the state-of-the-art for the special and well-studied class of recharging bandits (also known as delay-dependent). In this attempt, we develop new tools and insights for this class of problems, including a novel higher-dimensional relaxation and the technique of mirroring the evolution of virtual states. We believe that these novel elements could potentially be used for approaching richer classes of action-induced nonstationary bandits (e.g., special instances of restless bandits). In the case where the model parameters are initially unknown, we develop an online learning adaptation of our algorithm for which we provide sublinear regret guarantees against its full-information counterpart.

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.

We propose a novel approach to addressing two fundamental challenges in Model-based Reinforcement Learning (MBRL): the computational expense of repeatedly finding a good policy in the learned model, and the objective mismatch between model fitting and policy computation. Our "lazy" method leverages a novel unified objective, Performance Difference via Advantage in Model, to capture the performance difference between the learned policy and expert policy under the true dynamics. This objective demonstrates that optimizing the expected policy advantage in the learned model under an exploration distribution is sufficient for policy computation, resulting in a significant boost in computational efficiency compared to traditional planning methods. Additionally, the unified objective uses a value moment matching term for model fitting, which is aligned with the model's usage during policy computation. We present two no-regret algorithms to optimize the proposed objective, and demonstrate their statistical and computational gains compared to existing MBRL methods through simulated benchmarks.

Unsupervised reinforcement learning (RL) studies how to leverage environment statistics to learn useful behaviors without the cost of reward engineering. However, a central challenge in unsupervised RL is to extract behaviors that meaningfully affect the world and cover the range of possible outcomes, without getting distracted by inherently unpredictable, uncontrollable, and stochastic elements in the environment. To this end, we propose an unsupervised RL method designed for high-dimensional, stochastic environments based on an adversarial game between two policies (which we call Explore and Control) controlling a single body and competing over the amount of observation entropy the agent experiences. The Explore agent seeks out states that maximally surprise the Control agent, which in turn aims to minimize surprise, and thereby manipulate the environment to return to familiar and predictable states. The competition between these two policies drives them to seek out increasingly surprising parts of the environment while learning to gain mastery over them. We show formally that the resulting algorithm maximizes coverage of the underlying state in block MDPs with stochastic observations, providing theoretical backing to our hypothesis that this procedure avoids uncontrollable and stochastic distractions. Our experiments further demonstrate that Adversarial Surprise leads to the emergence of complex and meaningful skills, and outperforms state-of-the-art unsupervised reinforcement learning methods in terms of both exploration and zero-shot transfer to downstream tasks.

These lecture notes give a statistical perspective on the foundations of reinforcement learning and interactive decision making. We present a unifying framework for addressing the exploration-exploitation dilemma using frequentist and Bayesian approaches, with connections and parallels between supervised learning/estimation and decision making as an overarching theme. Special attention is paid to function approximation and flexible model classes such as neural networks. Topics covered include multi-armed and contextual bandits, structured bandits, and reinforcement learning with high-dimensional feedback.

Preference-based feedback is important for many applications in machine learning where evaluation of a reward function is not feasible. Notable recent examples arise in preference alignment for large language models, including in reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO). For many applications of preference alignment, the cost of acquiring human feedback can be substantial. In this work, we take advantage of the fact that one can often choose contexts at which to obtain human feedback to most efficiently identify a good policy, and formalize the setting as an active contextual dueling bandit problem. We propose an active exploration algorithm to efficiently select the data and provide theoretical proof that it has a polynomial worst-case regret bound. We extend the setting and methodology for practical use in preference alignment of large language models. We provide two extensions, an online and an offline approach. Our method outperforms the baselines with limited samples of human preferences on several language models and four real-world datasets including two new datasets that we contribute to the literature.

Decision-making under distribution shift is a central challenge in reinforcement learning (RL), where training and deployment environments differ. We study this problem through the lens of robust Markov decision processes (RMDPs), which optimize performance against adversarial transition dynamics. Our focus is the online setting, where the agent has only limited interaction with the environment, making sample efficiency and exploration especially critical. Policy optimization, despite its success in standard RL, remains theoretically and empirically underexplored in robust RL. To bridge this gap, we propose Distributionally Robust Regularized Policy Optimization algorithm (DR-RPO), a model-free online policy optimization method that learns robust policies with sublinear regret. To enable tractable optimization within the softmax policy class, DR-RPO incorporates reference-policy regularization, yielding RMDP variants that are doubly constrained in both transitions and policies. To scale to large state-action spaces, we adopt the d-rectangular linear MDP formulation and combine linear function approximation with an upper confidence bonus for optimistic exploration. We provide theoretical guarantees showing that policy optimization can achieve polynomial suboptimality bounds and sample efficiency in robust RL, matching the performance of value-based approaches. Finally, empirical results across diverse domains corroborate our theory and demonstrate the robustness of DR-RPO.

In this paper we address the solution of the popular Wordle puzzle, using new reinforcement learning methods, which apply more generally to adaptive control of dynamic systems and to classes of Partially Observable Markov Decision Process (POMDP) problems. These methods are based on approximation in value space and the rollout approach, admit a straightforward implementation, and provide improved performance over various heuristic approaches. For the Wordle puzzle, they yield on-line solution strategies that are very close to optimal at relatively modest computational cost. Our methods are viable for more complex versions of Wordle and related search problems, for which an optimal strategy would be impossible to compute. They are also applicable to a wide range of adaptive sequential decision problems that involve an unknown or frequently changing environment whose parameters are estimated on-line.

The emergence of Multimodal Large Language Models (MLLMs) has propelled the development of autonomous agents that operate on Graphical User Interfaces (GUIs) using pure visual input. A fundamental challenge is robustly grounding natural language instructions. This requires a precise spatial alignment, which accurately locates the coordinates of each element, and, more critically, a correct semantic alignment, which matches the instructions to the functionally appropriate UI element. Although Reinforcement Learning with Verifiable Rewards (RLVR) has proven to be effective at improving spatial alignment for these MLLMs, we find that inefficient exploration bottlenecks semantic alignment, which prevent models from learning difficult semantic associations. To address this exploration problem, we present Adaptive Exploration Policy Optimization (AEPO), a new policy optimization framework. AEPO employs a multi-answer generation strategy to enforce broader exploration, which is then guided by a theoretically grounded Adaptive Exploration Reward (AER) function derived from first principles of efficiency eta=U/C. Our AEPO-trained models, InfiGUI-G1-3B and InfiGUI-G1-7B, establish new state-of-the-art results across multiple challenging GUI grounding benchmarks, achieving significant relative improvements of up to 9.0% against the naive RLVR baseline on benchmarks designed to test generalization and semantic understanding. Resources are available at https://github.com/InfiXAI/InfiGUI-G1.

We investigate the problem of stochastic, combinatorial multi-armed bandits where the learner only has access to bandit feedback and the reward function can be non-linear. We provide a general framework for adapting discrete offline approximation algorithms into sublinear alpha-regret methods that only require bandit feedback, achieving Oleft(T^2{3}log(T)^1{3}right) expected cumulative alpha-regret dependence on the horizon T. The framework only requires the offline algorithms to be robust to small errors in function evaluation. The adaptation procedure does not even require explicit knowledge of the offline approximation algorithm -- the offline algorithm can be used as black box subroutine. To demonstrate the utility of the proposed framework, the proposed framework is applied to multiple problems in submodular maximization, adapting approximation algorithms for cardinality and for knapsack constraints. The new CMAB algorithms for knapsack constraints outperform a full-bandit method developed for the adversarial setting in experiments with real-world data.

Bayesian Optimization (BO) is typically used to optimize an unknown function f that is noisy and costly to evaluate, by exploiting an acquisition function that must be maximized at each optimization step. Even if provably asymptotically optimal BO algorithms are efficient at optimizing low-dimensional functions, scaling them to high-dimensional spaces remains an open problem, often tackled by assuming an additive structure for f. By doing so, BO algorithms typically introduce additional restrictive assumptions on the additive structure that reduce their applicability domain. This paper contains two main contributions: (i) we relax the restrictive assumptions on the additive structure of f without weakening the maximization guarantees of the acquisition function, and (ii) we address the over-exploration problem for decentralized BO algorithms. To these ends, we propose DuMBO, an asymptotically optimal decentralized BO algorithm that achieves very competitive performance against state-of-the-art BO algorithms, especially when the additive structure of f comprises high-dimensional factors.

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

The performance of acquisition functions for Bayesian optimisation to locate the global optimum of continuous functions is investigated in terms of the Pareto front between exploration and exploitation. We show that Expected Improvement (EI) and the Upper Confidence Bound (UCB) always select solutions to be expensively evaluated on the Pareto front, but Probability of Improvement is not guaranteed to do so and Weighted Expected Improvement does so only for a restricted range of weights. We introduce two novel epsilon-greedy acquisition functions. Extensive empirical evaluation of these together with random search, purely exploratory, and purely exploitative search on 10 benchmark problems in 1 to 10 dimensions shows that epsilon-greedy algorithms are generally at least as effective as conventional acquisition functions (e.g., EI and UCB), particularly with a limited budget. In higher dimensions epsilon-greedy approaches are shown to have improved performance over conventional approaches. These results are borne out on a real world computational fluid dynamics optimisation problem and a robotics active learning problem. Our analysis and experiments suggest that the most effective strategy, particularly in higher dimensions, is to be mostly greedy, occasionally selecting a random exploratory solution.

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

Recently, the study of linear misspecified bandits has generated intriguing implications of the hardness of learning in bandits and reinforcement learning (RL). In particular, Du et al. (2020) show that even if a learner is given linear features in R^d that approximate the rewards in a bandit or RL with a uniform error of varepsilon, searching for an O(varepsilon)-optimal action requires pulling at least Omega(exp(d)) queries. Furthermore, Lattimore et al. (2020) show that a degraded O(varepsilond)-optimal solution can be learned within poly(d/varepsilon) queries. Yet it is unknown whether a structural assumption on the ground-truth parameter, such as sparsity, could break the varepsilond barrier. In this paper, we address this question by showing that algorithms can obtain O(varepsilon)-optimal actions by querying O(varepsilon^{-s}d^s) actions, where s is the sparsity parameter, removing the exp(d)-dependence. We then establish information-theoretical lower bounds, i.e., Omega(exp(s)), to show that our upper bound on sample complexity is nearly tight if one demands an error O(s^{delta}varepsilon) for 0<delta<1. For deltageq 1, we further show that poly(s/varepsilon) queries are possible when the linear features are "good" and even in general settings. These results provide a nearly complete picture of how sparsity can help in misspecified bandit learning and provide a deeper understanding of when linear features are "useful" for bandit and reinforcement learning with misspecification.

Curiosity-based reward schemes can present powerful exploration mechanisms which facilitate the discovery of solutions for complex, sparse or long-horizon tasks. However, as the agent learns to reach previously unexplored spaces and the objective adapts to reward new areas, many behaviours emerge only to disappear due to being overwritten by the constantly shifting objective. We argue that merely using curiosity for fast environment exploration or as a bonus reward for a specific task does not harness the full potential of this technique and misses useful skills. Instead, we propose to shift the focus towards retaining the behaviours which emerge during curiosity-based learning. We posit that these self-discovered behaviours serve as valuable skills in an agent's repertoire to solve related tasks. Our experiments demonstrate the continuous shift in behaviour throughout training and the benefits of a simple policy snapshot method to reuse discovered behaviour for transfer tasks.

We present a novel unified bilevel optimization-based framework, PARL, formulated to address the recently highlighted critical issue of policy alignment in reinforcement learning using utility or preference-based feedback. We identify a major gap within current algorithmic designs for solving policy alignment due to a lack of precise characterization of the dependence of the alignment objective on the data generated by policy trajectories. This shortfall contributes to the sub-optimal performance observed in contemporary algorithms. Our framework addressed these concerns by explicitly parameterizing the distribution of the upper alignment objective (reward design) by the lower optimal variable (optimal policy for the designed reward). Interestingly, from an optimization perspective, our formulation leads to a new class of stochastic bilevel problems where the stochasticity at the upper objective depends upon the lower-level variable. To demonstrate the efficacy of our formulation in resolving alignment issues in RL, we devised an algorithm named A-PARL to solve PARL problem, establishing sample complexity bounds of order O(1/T). Our empirical results substantiate that the proposed PARL can address the alignment concerns in RL by showing significant improvements (up to 63\% in terms of required samples) for policy alignment in large-scale environments of the Deepmind control suite and Meta world tasks.

Despite their success in many domains, large language models (LLMs) remain under-studied in scenarios requiring optimal decision-making under uncertainty. This is crucial as many real-world applications, ranging from personalized recommendations to healthcare interventions, demand that LLMs not only predict but also actively learn to make optimal decisions through exploration. In this work, we measure LLMs' (in)ability to make optimal decisions in bandits, a state-less reinforcement learning setting relevant to many applications. We develop a comprehensive suite of environments, including both context-free and contextual bandits with varying task difficulties, to benchmark LLMs' performance. Motivated by the existence of optimal exploration algorithms, we propose efficient ways to integrate this algorithmic knowledge into LLMs: by providing explicit algorithm-guided support during inference; and through algorithm distillation via in-context demonstrations and fine-tuning, using synthetic data generated from these algorithms. Impressively, these techniques allow us to achieve superior exploration performance with smaller models, surpassing larger models on various tasks. We conducted an extensive ablation study to shed light on various factors, such as task difficulty and data representation, that influence the efficiency of LLM exploration. Additionally, we conduct a rigorous analysis of the LLM's exploration efficiency using the concept of regret, linking its ability to explore to the model size and underlying algorithm.

Model-based deep reinforcement learning has achieved success in various domains that require high sample efficiencies, such as Go and robotics. However, there are some remaining issues, such as planning efficient explorations to learn more accurate dynamic models, evaluating the uncertainty of the learned models, and more rational utilization of models. To mitigate these issues, we present MEEE, a model-ensemble method that consists of optimistic exploration and weighted exploitation. During exploration, unlike prior methods directly selecting the optimal action that maximizes the expected accumulative return, our agent first generates a set of action candidates and then seeks out the optimal action that takes both expected return and future observation novelty into account. During exploitation, different discounted weights are assigned to imagined transition tuples according to their model uncertainty respectively, which will prevent model predictive error propagation in agent training. Experiments on several challenging continuous control benchmark tasks demonstrated that our approach outperforms other model-free and model-based state-of-the-art methods, especially in sample complexity.

We propose a new method for count-based exploration in high-dimensional state spaces. Unlike previous work which relies on density models, we show that counts can be derived by averaging samples from the Rademacher distribution (or coin flips). This insight is used to set up a simple supervised learning objective which, when optimized, yields a state's visitation count. We show that our method is significantly more effective at deducing ground-truth visitation counts than previous work; when used as an exploration bonus for a model-free reinforcement learning algorithm, it outperforms existing approaches on most of 9 challenging exploration tasks, including the Atari game Montezuma's Revenge.

Despite the recent success of representation learning in sequential decision making, the study of the pure exploration scenario (i.e., identify the best option and minimize the sample complexity) is still limited. In this paper, we study multi-task representation learning for best arm identification in linear bandits (RepBAI-LB) and best policy identification in contextual linear bandits (RepBPI-CLB), two popular pure exploration settings with wide applications, e.g., clinical trials and web content optimization. In these two problems, all tasks share a common low-dimensional linear representation, and our goal is to leverage this feature to accelerate the best arm (policy) identification process for all tasks. For these problems, we design computationally and sample efficient algorithms DouExpDes and C-DouExpDes, which perform double experimental designs to plan optimal sample allocations for learning the global representation. We show that by learning the common representation among tasks, our sample complexity is significantly better than that of the native approach which solves tasks independently. To the best of our knowledge, this is the first work to demonstrate the benefits of representation learning for multi-task pure exploration.

We tackle real-world problems with complex structures beyond the pixel-based game or simulator. We formulate it as a few-shot reinforcement learning problem where a task is characterized by a subtask graph that defines a set of subtasks and their dependencies that are unknown to the agent. Different from the previous meta-rl methods trying to directly infer the unstructured task embedding, our multi-task subtask graph inferencer (MTSGI) first infers the common high-level task structure in terms of the subtask graph from the training tasks, and use it as a prior to improve the task inference in testing. Our experiment results on 2D grid-world and complex web navigation domains show that the proposed method can learn and leverage the common underlying structure of the tasks for faster adaptation to the unseen tasks than various existing algorithms such as meta reinforcement learning, hierarchical reinforcement learning, and other heuristic agents.

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

Simple regret is a natural and parameter-free performance criterion for pure exploration in multi-armed bandits yet is less popular than the probability of missing the best arm or an epsilon-good arm, perhaps due to lack of easy ways to characterize it. In this paper, we make significant progress on minimizing simple regret in both data-rich (Tge n) and data-poor regime (T le n) where n is the number of arms, and T is the number of samples. At its heart is our improved instance-dependent analysis of the well-known Sequential Halving (SH) algorithm, where we bound the probability of returning an arm whose mean reward is not within epsilon from the best (i.e., not epsilon-good) for any choice of epsilon>0, although epsilon is not an input to SH. Our bound not only leads to an optimal worst-case simple regret bound of n/T up to logarithmic factors but also essentially matches the instance-dependent lower bound for returning an epsilon-good arm reported by Katz-Samuels and Jamieson (2020). For the more challenging data-poor regime, we propose Bracketing SH (BSH) that enjoys the same improvement even without sampling each arm at least once. Our empirical study shows that BSH outperforms existing methods on real-world tasks.

Balancing exploration and exploitation remains a central challenge in reinforcement learning with verifiable rewards (RLVR) for large language models (LLMs). Current RLVR methods often overemphasize exploitation, leading to entropy collapse, diminished exploratory capacity, and ultimately limited performance gains. Although techniques that increase policy stochasticity can promote exploration, they frequently fail to escape dominant behavioral modes. This creates a self-reinforcing loop-repeatedly sampling and rewarding dominant modes-that further erodes exploration. We introduce Exploration-Enhanced Policy Optimization (EEPO), a framework that promotes exploration via two-stage rollouts with adaptive unlearning. In the first stage, the model generates half of the trajectories; it then undergoes a lightweight unlearning step to temporarily suppress these sampled responses, forcing the second stage to explore different regions of the output space. This sample-then-forget mechanism disrupts the self-reinforcing loop and promotes wider exploration during rollouts. Across five reasoning benchmarks, EEPO outperforms GRPO, achieving average relative gains of 24.3% on Qwen2.5-3B, 33.0% on Llama3.2-3B-Instruct, and 10.4% on Qwen3-8B-Base.

We consider learning to play multiplayer imperfect-information games with simultaneous moves and large state-action spaces. Previous attempts to tackle such challenging games have largely focused on model-free learning methods, often requiring hundreds of years of experience to produce competitive agents. Our approach is based on model-based planning. We tackle the problem of partial observability by first building an (oracle) planner that has access to the full state of the environment and then distilling the knowledge of the oracle to a (follower) agent which is trained to play the imperfect-information game by imitating the oracle's choices. We experimentally show that planning with naive Monte Carlo tree search does not perform very well in large combinatorial action spaces. We therefore propose planning with a fixed-depth tree search and decoupled Thompson sampling for action selection. We show that the planner is able to discover efficient playing strategies in the games of Clash Royale and Pommerman and the follower policy successfully learns to implement them by training on a few hundred battles.

While Large Language Models (LLMs) hold promise to become autonomous agents, they often explore suboptimally in sequential decision-making. Recent work has sought to enhance this capability via supervised fine-tuning (SFT) or reinforcement learning (RL), improving regret on the classic multi-armed bandit task. However, it remains unclear how these learning methods shape exploration strategies and how well they generalize. We investigate both paradigms by training LLMs with SFT on expert trajectories and RL with a range of tailored reward signals including a strategic, regret-shaped reward to reduce variance, and an algorithmic reward that enables oracle imitation. The resulting agents outperform pre-trained models and achieve performance comparable to Upper Confidence Bound (UCB) and Thompson Sampling, with robust generalization to 6x longer horizons and across bandit families. Behavioral analysis reveals that gains often stem from more sophisticated but greedier exploitation: RL/SFT agents are more prone to early catastrophic failure than pre-trained models, prematurely abandoning exploration. Furthermore, agents trained to imitate UCB learn to outperform their teacher by adopting more exploitative variants. Our findings clarify when each training paradigm is preferable and advocate tailored reward design and evaluation beyond average regret to promote robust exploratory behavior.

Learning to play optimally against any mixture over a diverse set of strategies is of important practical interests in competitive games. In this paper, we propose simplex-NeuPL that satisfies two desiderata simultaneously: i) learning a population of strategically diverse basis policies, represented by a single conditional network; ii) using the same network, learn best-responses to any mixture over the simplex of basis policies. We show that the resulting conditional policies incorporate prior information about their opponents effectively, enabling near optimal returns against arbitrary mixture policies in a game with tractable best-responses. We verify that such policies behave Bayes-optimally under uncertainty and offer insights in using this flexibility at test time. Finally, we offer evidence that learning best-responses to any mixture policies is an effective auxiliary task for strategic exploration, which, by itself, can lead to more performant populations.

Reinforcement learning (RL) is a promising approach for robotic manipulation, but it can suffer from low sample efficiency and requires extensive exploration of large state-action spaces. Recent methods leverage the commonsense knowledge and reasoning abilities of large language models (LLMs) to guide exploration toward more meaningful states. However, LLMs can produce plans that are semantically plausible yet physically infeasible, yielding unreliable behavior. We introduce LLM-TALE, a framework that uses LLMs' planning to directly steer RL exploration. LLM-TALE integrates planning at both the task level and the affordance level, improving learning efficiency by directing agents toward semantically meaningful actions. Unlike prior approaches that assume optimal LLM-generated plans or rewards, LLM-TALE corrects suboptimality online and explores multimodal affordance-level plans without human supervision. We evaluate LLM-TALE on pick-and-place tasks in standard RL benchmarks, observing improvements in both sample efficiency and success rates over strong baselines. Real-robot experiments indicate promising zero-shot sim-to-real transfer. Code and supplementary material are available at https://llm-tale.github.io.

In this paper, we conduct a holistic exploration of the Universal Decompositional Semantic (UDS) Parsing. We first introduce a cascade model for UDS parsing that decomposes the complex parsing task into semantically appropriate subtasks. Our approach outperforms the prior models, while significantly reducing inference time. We also incorporate syntactic information and further optimized the architecture. Besides, different ways for data augmentation are explored, which further improve the UDS Parsing. Lastly, we conduct experiments to investigate the efficacy of ChatGPT in handling the UDS task, revealing that it excels in attribute parsing but struggles in relation parsing, and using ChatGPT for data augmentation yields suboptimal results. Our code is available at https://github.com/hexuandeng/HExp4UDS.

Ensuring sufficient exploration is a central challenge when training meta-reinforcement learning (meta-RL) agents to solve novel environments. Conventional solutions to the exploration-exploitation dilemma inject explicit incentives such as randomization, uncertainty bonuses, or intrinsic rewards to encourage exploration. In this work, we hypothesize that an agent trained solely to maximize a greedy (exploitation-only) objective can nonetheless exhibit emergent exploratory behavior, provided three conditions are met: (1) Recurring Environmental Structure, where the environment features repeatable regularities that allow past experience to inform future choices; (2) Agent Memory, enabling the agent to retain and utilize historical interaction data; and (3) Long-Horizon Credit Assignment, where learning propagates returns over a time frame sufficient for the delayed benefits of exploration to inform current decisions. Through experiments in stochastic multi-armed bandits and temporally extended gridworlds, we observe that, when both structure and memory are present, a policy trained on a strictly greedy objective exhibits information-seeking exploratory behavior. We further demonstrate, through controlled ablations, that emergent exploration vanishes if either environmental structure or agent memory is absent (Conditions 1 & 2). Surprisingly, removing long-horizon credit assignment (Condition 3) does not always prevent emergent exploration-a result we attribute to the pseudo-Thompson Sampling effect. These findings suggest that, under the right prerequisites, exploration and exploitation need not be treated as orthogonal objectives but can emerge from a unified reward-maximization process.

Vision-Language-Action (VLA) models, trained via flow-matching or diffusion objectives, excel at learning complex behaviors from large-scale, multi-modal datasets (e.g., human teleoperation, scripted policies). However, since VLAs incorporate diverse data modes in the pre-training stage, and the finetuning dataset often contains demonstration data collected in a kinematically suboptimal or undesirable way, it exists redundant action modes that are irrelevant to the success action modes of the downstream task. Specifically, we observe a critical inference-time fragility among various sampled noises after supervised finetuning of pre-trained VLAs. In this paper, we attribute this instability to the distribution shift between the VLA policy and the policy induced by stable success modes of the downstream task dataset. Thus, we propose TACO, a test-time-scaling (TTS) framework that applies a lightweight pseudo-count estimator as a high-fidelity verifier of action chunks. The VLA models integrated with TACO can execute the actions with maximum pseudo-count from all sampled action chunks, thereby preventing distribution shifts while preserving the generalization ability of VLAs since the constraint is applied only during inference. Our method resembles the classical anti-exploration principle in offline reinforcement learning (RL), and being gradient-free, it incurs significant computational benefits compared to RL update, especially for flow or diffusion-based VLAs which are difficult to perform RL update due to denoising process. Extensive experiments across four simulation benchmarks (RoboTwin2.0, Robotwin, LIBERO, SimplerEnv) and a dual-arm platform demonstrate that our method significantly improves the inference stability and success rates in downstream-task adaptations.

Unsupervised pretraining has been transformative in many supervised domains. However, applying such ideas to reinforcement learning (RL) presents a unique challenge in that fine-tuning does not involve mimicking task-specific data, but rather exploring and locating the solution through iterative self-improvement. In this work, we study how unlabeled prior trajectory data can be leveraged to learn efficient exploration strategies. While prior data can be used to pretrain a set of low-level skills, or as additional off-policy data for online RL, it has been unclear how to combine these ideas effectively for online exploration. Our method SUPE (Skills from Unlabeled Prior data for Exploration) demonstrates that a careful combination of these ideas compounds their benefits. Our method first extracts low-level skills using a variational autoencoder (VAE), and then pseudo-relabels unlabeled trajectories using an optimistic reward model, transforming prior data into high-level, task-relevant examples. Finally, SUPE uses these transformed examples as additional off-policy data for online RL to learn a high-level policy that composes pretrained low-level skills to explore efficiently. We empirically show that SUPE reliably outperforms prior strategies, successfully solving a suite of long-horizon, sparse-reward tasks. Code: https://github.com/rail-berkeley/supe.

Large Language Models (LLMs) are typically fine-tuned for reasoning tasks through a two-stage pipeline of Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL), a process fraught with catastrophic forgetting and suboptimal trade-offs between imitation and exploration. Recent single-stage methods attempt to unify SFT and RL using heuristics, but lack a principled mechanism for dynamically balancing the two paradigms. In this paper, we reframe this challenge through the theoretical lens of implicit rewards, viewing SFT and RL not as distinct methods but as complementary reward signals. We introduce Adaptive Meta Fine-Tuning (AMFT), a novel single-stage algorithm that learns the optimal balance between SFT's implicit, path-level reward and RL's explicit, outcome-based reward. The core of AMFT is a meta-gradient adaptive weight controller that treats the SFT-RL balance as a learnable parameter, dynamically optimizing it to maximize long-term task performance. This forward-looking approach, regularized by policy entropy for stability, autonomously discovers an effective training curriculum. We conduct a comprehensive evaluation on challenging benchmarks spanning mathematical reasoning, abstract visual reasoning (General Points), and vision-language navigation (V-IRL). AMFT consistently establishes a new state-of-the-art and demonstrats superior generalization on out-of-distribution (OOD) tasks. Ablation studies and training dynamic analysis confirm that the meta-learning controller is crucial for AMFT's stability, sample efficiency, and performance, offering a more principled and effective paradigm for LLM alignment.Our codes are open-sourced via https://github.com/hlxtsyj/AMFT.

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

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.

Recent advancements in meta-learning have enabled the automatic discovery of novel reinforcement learning algorithms parameterized by surrogate objective functions. To improve upon manually designed algorithms, the parameterization of this learned objective function must be expressive enough to represent novel principles of learning (instead of merely recovering already established ones) while still generalizing to a wide range of settings outside of its meta-training distribution. However, existing methods focus on discovering objective functions that, like many widely used objective functions in reinforcement learning, do not take into account the total number of steps allowed for training, or "training horizon". In contrast, humans use a plethora of different learning objectives across the course of acquiring a new ability. For instance, students may alter their studying techniques based on the proximity to exam deadlines and their self-assessed capabilities. This paper contends that ignoring the optimization time horizon significantly restricts the expressive potential of discovered learning algorithms. We propose a simple augmentation to two existing objective discovery approaches that allows the discovered algorithm to dynamically update its objective function throughout the agent's training procedure, resulting in expressive schedules and increased generalization across different training horizons. In the process, we find that commonly used meta-gradient approaches fail to discover such adaptive objective functions while evolution strategies discover highly dynamic learning rules. We demonstrate the effectiveness of our approach on a wide range of tasks and analyze the resulting learned algorithms, which we find effectively balance exploration and exploitation by modifying the structure of their learning rules throughout the agent's lifetime.

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

Automated red-teaming has become a crucial approach for uncovering vulnerabilities in large language models (LLMs). However, most existing methods focus on isolated safety flaws, limiting their ability to adapt to dynamic defenses and uncover complex vulnerabilities efficiently. To address this challenge, we propose Auto-RT, a reinforcement learning framework that automatically explores and optimizes complex attack strategies to effectively uncover security vulnerabilities through malicious queries. Specifically, we introduce two key mechanisms to reduce exploration complexity and improve strategy optimization: 1) Early-terminated Exploration, which accelerate exploration by focusing on high-potential attack strategies; and 2) Progressive Reward Tracking algorithm with intermediate downgrade models, which dynamically refine the search trajectory toward successful vulnerability exploitation. Extensive experiments across diverse LLMs demonstrate that, by significantly improving exploration efficiency and automatically optimizing attack strategies, Auto-RT detects a boarder range of vulnerabilities, achieving a faster detection speed and 16.63\% higher success rates compared to existing methods.

Motivated by concerns about making online decisions that incur undue amount of risk at each time step, in this paper, we formulate the probably anytime-safe stochastic combinatorial semi-bandits problem. In this problem, the agent is given the option to select a subset of size at most K from a set of L ground items. Each item is associated to a certain mean reward as well as a variance that represents its risk. To mitigate the risk that the agent incurs, we require that with probability at least 1-delta, over the entire horizon of time T, each of the choices that the agent makes should contain items whose sum of variances does not exceed a certain variance budget. We call this probably anytime-safe constraint. Under this constraint, we design and analyze an algorithm {\sc PASCombUCB} that minimizes the regret over the horizon of time T. By developing accompanying information-theoretic lower bounds, we show that under both the problem-dependent and problem-independent paradigms, {\sc PASCombUCB} is almost asymptotically optimal. Experiments are conducted to corroborate our theoretical findings. Our problem setup, the proposed {\sc PASCombUCB} algorithm, and novel analyses are applicable to domains such as recommendation systems and transportation in which an agent is allowed to choose multiple items at a single time step and wishes to control the risk over the whole time horizon.

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

This paper investigates conservative exploration in reinforcement learning where the performance of the learning agent is guaranteed to be above a certain threshold throughout the learning process. It focuses on the tabular episodic Markov Decision Process (MDP) setting that has finite states and actions. With the knowledge of an existing safe baseline policy, an algorithm termed as StepMix is proposed to balance the exploitation and exploration while ensuring that the conservative constraint is never violated in each episode with high probability. StepMix features a unique design of a mixture policy that adaptively and smoothly interpolates between the baseline policy and the optimistic policy. Theoretical analysis shows that StepMix achieves near-optimal regret order as in the constraint-free setting, indicating that obeying the stringent episode-wise conservative constraint does not compromise the learning performance. Besides, a randomization-based EpsMix algorithm is also proposed and shown to achieve the same performance as StepMix. The algorithm design and theoretical analysis are further extended to the setting where the baseline policy is not given a priori but must be learned from an offline dataset, and it is proved that similar conservative guarantee and regret can be achieved if the offline dataset is sufficiently large. Experiment results corroborate the theoretical analysis and demonstrate the effectiveness of the proposed conservative exploration strategies.

Monte Carlo Tree Search (MCTS) is a powerful algorithm for solving complex decision-making problems. This paper presents an optimized MCTS implementation applied to the FrozenLake environment, a classic reinforcement learning task characterized by stochastic transitions. The optimization leverages cumulative reward and visit count tables along with the Upper Confidence Bound for Trees (UCT) formula, resulting in efficient learning in a slippery grid world. We benchmark our implementation against other decision-making algorithms, including MCTS with Policy and Q-Learning, and perform a detailed comparison of their performance. The results demonstrate that our optimized approach effectively maximizes rewards and success rates while minimizing convergence time, outperforming baseline methods, especially in environments with inherent randomness.

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

The rapid development of large language and multimodal models has sparked significant interest in using proprietary models, such as GPT-4o, to develop autonomous agents capable of handling real-world scenarios like web navigation. Although recent open-source efforts have tried to equip agents with the ability to explore environments and continuously improve over time, they are building text-only agents in synthetic environments where the reward signals are clearly defined. Such agents struggle to generalize to realistic settings that require multimodal perception abilities and lack ground-truth signals. In this paper, we introduce an open-source framework designed to facilitate the development of multimodal web agent that can autonomously conduct real-world exploration and improve itself. We first train the base model with imitation learning to gain the basic abilities. We then let the agent explore the open web and collect feedback on its trajectories. After that, it further improves its policy by learning from well-performing trajectories judged by another general-purpose model. This exploration-feedback-optimization cycle can continue for several iterations. Experimental results show that our web agent successfully improves itself after each iteration, demonstrating strong performance across multiple test sets.

Reinforcement learning (RL) in continuous action spaces encounters persistent challenges, such as inefficient exploration and convergence to suboptimal solutions. To address these limitations, we propose CAMEL, a novel framework integrating LLM-generated suboptimal policies into the RL training pipeline. CAMEL leverages dynamic action masking and an adaptive epsilon-masking mechanism to guide exploration during early training stages while gradually enabling agents to optimize policies independently. At the core of CAMEL lies the integration of Python-executable suboptimal policies generated by LLMs based on environment descriptions and task objectives. Although simplistic and hard-coded, these policies offer valuable initial guidance for RL agents. To effectively utilize these priors, CAMEL employs masking-aware optimization to dynamically constrain the action space based on LLM outputs. Additionally, epsilon-masking gradually reduces reliance on LLM-generated guidance, enabling agents to transition from constrained exploration to autonomous policy refinement. Experimental validation on Gymnasium MuJoCo environments demonstrates the effectiveness of CAMEL. In Hopper-v4 and Ant-v4, LLM-generated policies significantly improve sample efficiency, achieving performance comparable to or surpassing expert masking baselines. For Walker2d-v4, where LLMs struggle to accurately model bipedal gait dynamics, CAMEL maintains robust RL performance without notable degradation, highlighting the framework's adaptability across diverse tasks. While CAMEL shows promise in enhancing sample efficiency and mitigating convergence challenges, these issues remain open for further research. Future work aims to generalize CAMEL to multimodal LLMs for broader observation-action spaces and automate policy evaluation, reducing human intervention and enhancing scalability in RL training pipelines.

Sparse reward environments in reinforcement learning (RL) pose significant challenges for exploration, often leading to inefficient or incomplete learning processes. To tackle this issue, this work proposes a teacher-student RL framework that leverages Large Language Models (LLMs) as "teachers" to guide the agent's learning process by decomposing complex tasks into subgoals. Due to their inherent capability to understand RL environments based on a textual description of structure and purpose, LLMs can provide subgoals to accomplish the task defined for the environment in a similar fashion to how a human would do. In doing so, three types of subgoals are proposed: positional targets relative to the agent, object representations, and language-based instructions generated directly by the LLM. More importantly, we show that it is possible to query the LLM only during the training phase, enabling agents to operate within the environment without any LLM intervention. We assess the performance of this proposed framework by evaluating three state-of-the-art open-source LLMs (Llama, DeepSeek, Qwen) eliciting subgoals across various procedurally generated environment of the MiniGrid benchmark. Experimental results demonstrate that this curriculum-based approach accelerates learning and enhances exploration in complex tasks, achieving up to 30 to 200 times faster convergence in training steps compared to recent baselines designed for sparse reward environments.

Large language model (LLM)-based agents have shown promise in tackling complex tasks by interacting dynamically with the environment. Existing work primarily focuses on behavior cloning from expert demonstrations or preference learning through exploratory trajectory sampling. However, these methods often struggle to address long-horizon tasks, where suboptimal actions accumulate step by step, causing agents to deviate from correct task trajectories. To address this, we highlight the importance of timely calibration and the need to automatically construct calibration trajectories for training agents. We propose Step-Level Trajectory Calibration (STeCa), a novel framework for LLM agent learning. Specifically, STeCa identifies suboptimal actions through a step-level reward comparison during exploration. It constructs calibrated trajectories using LLM-driven reflection, enabling agents to learn from improved decision-making processes. We finally leverage these calibrated trajectories with successful trajectories for reinforced training. Extensive experiments demonstrate that STeCa significantly outperforms existing methods. Further analysis highlights that timely calibration enables agents to complete tasks with greater robustness. Our code and data are available at https://github.com/WangHanLinHenry/STeCa.

Large language models (LLMs) have demonstrated powerful decision-making and planning capabilities in solving complicated real-world problems. LLM-based autonomous agents can interact with diverse tools (e.g., functional APIs) and generate solution plans that execute a series of API function calls in a step-by-step manner. The multitude of candidate API function calls significantly expands the action space, amplifying the critical need for efficient action space navigation. However, existing methods either struggle with unidirectional exploration in expansive action spaces, trapped into a locally optimal solution, or suffer from exhaustively traversing all potential actions, causing inefficient navigation. To address these issues, we propose ToolChain*, an efficient tree search-based planning algorithm for LLM-based agents. It formulates the entire action space as a decision tree, where each node represents a possible API function call involved in a solution plan. By incorporating the A* search algorithm with task-specific cost function design, it efficiently prunes high-cost branches that may involve incorrect actions, identifying the most low-cost valid path as the solution. Extensive experiments on multiple tool-use and reasoning tasks demonstrate that ToolChain* efficiently balances exploration and exploitation within an expansive action space. It outperforms state-of-the-art baselines on planning and reasoning tasks by 3.1% and 3.5% on average while requiring 7.35x and 2.31x less time, respectively.

We present Klear-Reasoner, a model with long reasoning capabilities that demonstrates careful deliberation during problem solving, achieving outstanding performance across multiple benchmarks. Although there are already many excellent works related to inference models in the current community, there are still many problems with reproducing high-performance inference models due to incomplete disclosure of training details. This report provides an in-depth analysis of the reasoning model, covering the entire post-training workflow from data preparation and long Chain-of-Thought supervised fine-tuning (long CoT SFT) to reinforcement learning (RL), along with detailed ablation studies for each experimental component. For SFT data, our experiments show that a small number of high-quality data sources are more effective than a large number of diverse data sources, and that difficult samples can achieve better results without accuracy filtering. In addition, we investigate two key issues with current clipping mechanisms in RL: Clipping suppresses critical exploration signals and ignores suboptimal trajectories. To address these challenges, we propose Gradient-Preserving clipping Policy Optimization (GPPO) that gently backpropagates gradients from clipped tokens. GPPO not only enhances the model's exploration capacity but also improves its efficiency in learning from negative samples. Klear-Reasoner exhibits exceptional reasoning abilities in mathematics and programming, scoring 90.5\% on AIME 2024, 83.2\% on AIME 2025, 66.0\% on LiveCodeBench V5 and 58.1\% on LiveCodeBench V6.

While Large Language Models (LLMs) have demonstrated remarkable capabilities across diverse natural language processing tasks, aligning these models with varying human preferences across multiple objectives remains a significant challenge in practical deployments. Existing multi-objective alignment methods rely on manually specified preference weights, which not only burden users with difficult preference specification tasks but also lead to suboptimal training efficiency due to exploration of irrelevant preference combinations. To alleviate these issues, we propose a novel framework named PRO, i.e., PReference Orchestrator, which features a lightweight preference adapter that automatically infers prompt-specific preference weights during both training and deployment phases. Specifically, the adapter automatically learns appropriate preference weights for each prompt by training on normalized reward scores from multiple reward models for preferred responses, which inherently reflect effective preference balances across objectives. Additionally, We provide theoretical analysis proving that our prompt-aware preference mechanism achieves superior performance compared to fixed preference weights in multi-objective alignment scenarios. Extensive experiments across multiple tasks demonstrate the effectiveness of our method over existing multi-objective alignment approaches.

Large Language Model (LLM)-based agents have recently shown impressive capabilities in complex reasoning and tool use via multi-step interactions with their environments. While these agents have the potential to tackle complicated tasks, their problem-solving process, i.e., agents' interaction trajectory leading to task completion, remains underexploited. These trajectories contain rich feedback that can navigate agents toward the right directions for solving problems correctly. Although prevailing approaches, such as Monte Carlo Tree Search (MCTS), can effectively balance exploration and exploitation, they ignore the interdependence among various trajectories and lack the diversity of search spaces, which leads to redundant reasoning and suboptimal outcomes. To address these challenges, we propose SE-Agent, a Self-Evolution framework that enables Agents to optimize their reasoning processes iteratively. Our approach revisits and enhances former pilot trajectories through three key operations: revision, recombination, and refinement. This evolutionary mechanism enables two critical advantages: (1) it expands the search space beyond local optima by intelligently exploring diverse solution paths guided by previous trajectories, and (2) it leverages cross-trajectory inspiration to efficiently enhance performance while mitigating the impact of suboptimal reasoning paths. Through these mechanisms, SE-Agent achieves continuous self-evolution that incrementally improves reasoning quality. We evaluate SE-Agent on SWE-bench Verified to resolve real-world GitHub issues. Experimental results across five strong LLMs show that integrating SE-Agent delivers up to 55% relative improvement, achieving state-of-the-art performance among all open-source agents on SWE-bench Verified. Our code and demonstration materials are publicly available at https://github.com/JARVIS-Xs/SE-Agent.