Daily Papers

Understanding, navigating, and exploring the 3D physical real world has long been a central challenge in the development of artificial intelligence. In this work, we take a step toward this goal by introducing GenEx, a system capable of planning complex embodied world exploration, guided by its generative imagination that forms priors (expectations) about the surrounding environments. GenEx generates an entire 3D-consistent imaginative environment from as little as a single RGB image, bringing it to life through panoramic video streams. Leveraging scalable 3D world data curated from Unreal Engine, our generative model is rounded in the physical world. It captures a continuous 360-degree environment with little effort, offering a boundless landscape for AI agents to explore and interact with. GenEx achieves high-quality world generation, robust loop consistency over long trajectories, and demonstrates strong 3D capabilities such as consistency and active 3D mapping. Powered by generative imagination of the world, GPT-assisted agents are equipped to perform complex embodied tasks, including both goal-agnostic exploration and goal-driven navigation. These agents utilize predictive expectation regarding unseen parts of the physical world to refine their beliefs, simulate different outcomes based on potential decisions, and make more informed choices. In summary, we demonstrate that GenEx provides a transformative platform for advancing embodied AI in imaginative spaces and brings potential for extending these capabilities to real-world exploration.

Active Geo-localization (AGL) is the task of localizing a goal, represented in various modalities (e.g., aerial images, ground-level images, or text), within a predefined search area. Current methods approach AGL as a goal-reaching reinforcement learning (RL) problem with a distance-based reward. They localize the goal by implicitly learning to minimize the relative distance from it. However, when distance estimation becomes challenging or when encountering unseen targets and environments, the agent exhibits reduced robustness and generalization ability due to the less reliable exploration strategy learned during training. In this paper, we propose GeoExplorer, an AGL agent that incorporates curiosity-driven exploration through intrinsic rewards. Unlike distance-based rewards, our curiosity-driven reward is goal-agnostic, enabling robust, diverse, and contextually relevant exploration based on effective environment modeling. These capabilities have been proven through extensive experiments across four AGL benchmarks, demonstrating the effectiveness and generalization ability of GeoExplorer in diverse settings, particularly in localizing unfamiliar targets and environments.

We introduce a generic strategy for provably efficient multi-goal exploration. It relies on AdaGoal, a novel goal selection scheme that leverages a measure of uncertainty in reaching states to adaptively target goals that are neither too difficult nor too easy. We show how AdaGoal can be used to tackle the objective of learning an ε-optimal goal-conditioned policy for the (initially unknown) set of goal states that are reachable within L steps in expectation from a reference state s_0 in a reward-free Markov decision process. In the tabular case with S states and A actions, our algorithm requires O(L^3 S A ε^{-2}) exploration steps, which is nearly minimax optimal. We also readily instantiate AdaGoal in linear mixture Markov decision processes, yielding the first goal-oriented PAC guarantee with linear function approximation. Beyond its strong theoretical guarantees, we anchor AdaGoal in goal-conditioned deep reinforcement learning, both conceptually and empirically, by connecting its idea of selecting "uncertain" goals to maximizing value ensemble disagreement.

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.

One of the challenges in online reinforcement learning (RL) is that the agent needs to trade off the exploration of the environment and the exploitation of the samples to optimize its behavior. Whether we optimize for regret, sample complexity, state-space coverage or model estimation, we need to strike a different exploration-exploitation trade-off. In this paper, we propose to tackle the exploration-exploitation problem following a decoupled approach composed of: 1) An "objective-specific" algorithm that (adaptively) prescribes how many samples to collect at which states, as if it has access to a generative model (i.e., a simulator of the environment); 2) An "objective-agnostic" sample collection exploration strategy responsible for generating the prescribed samples as fast as possible. Building on recent methods for exploration in the stochastic shortest path problem, we first provide an algorithm that, given as input the number of samples b(s,a) needed in each state-action pair, requires O(B D + D^{3/2} S^2 A) time steps to collect the B=sum_{s,a} b(s,a) desired samples, in any unknown communicating MDP with S states, A actions and diameter D. Then we show how this general-purpose exploration algorithm can be paired with "objective-specific" strategies that prescribe the sample requirements to tackle a variety of settings -- e.g., model estimation, sparse reward discovery, goal-free cost-free exploration in communicating MDPs -- for which we obtain improved or novel sample complexity guarantees.

Realistic environments often provide agents with very limited feedback. When the environment is initially unknown, the feedback, in the beginning, can be completely absent, and the agents may first choose to devote all their effort on exploring efficiently. The exploration remains a challenge while it has been addressed with many hand-tuned heuristics with different levels of generality on one side, and a few theoretically-backed exploration strategies on the other. Many of them are incarnated by intrinsic motivation and in particular explorations bonuses. A common rule of thumb for exploration bonuses is to use 1/n bonus that is added to the empirical estimates of the reward, where n is a number of times this particular state (or a state-action pair) was visited. We show that, surprisingly, for a pure-exploration objective of reward-free exploration, bonuses that scale with 1/n bring faster learning rates, improving the known upper bounds with respect to the dependence on the horizon H. Furthermore, we show that with an improved analysis of the stopping time, we can improve by a factor H the sample complexity in the best-policy identification setting, which is another pure-exploration objective, where the environment provides rewards but the agent is not penalized for its behavior during the exploration phase.

We investigate the exploration of an unknown environment when no reward function is provided. Building on the incremental exploration setting introduced by Lim and Auer [1], we define the objective of learning the set of ε-optimal goal-conditioned policies attaining all states that are incrementally reachable within L steps (in expectation) from a reference state s_0. In this paper, we introduce a novel model-based approach that interleaves discovering new states from s_0 and improving the accuracy of a model estimate that is used to compute goal-conditioned policies to reach newly discovered states. The resulting algorithm, DisCo, achieves a sample complexity scaling as O(L^5 S_{L+ε} Γ_{L+ε} A ε^{-2}), where A is the number of actions, S_{L+ε} is the number of states that are incrementally reachable from s_0 in L+ε steps, and Γ_{L+ε} is the branching factor of the dynamics over such states. This improves over the algorithm proposed in [1] in both ε and L at the cost of an extra Γ_{L+ε} factor, which is small in most environments of interest. Furthermore, DisCo is the first algorithm that can return an ε/c_{min}-optimal policy for any cost-sensitive shortest-path problem defined on the L-reachable states with minimum cost c_{min}. Finally, we report preliminary empirical results confirming our theoretical findings.

Goal-oriented language-guided navigation requires robust exploration capabilities for agents to navigate to specified goals in unknown environments without step-by-step instructions. Existing methods tend to exclusively utilize shortest-path trajectories, lacking effective exploration priors for training navigation agents. To address the above challenges, we present SID, a goal-oriented language-guided navigation learning approach with Self-Improving Demonstrations. Specifically, SID learns an initial agent on the shortest-path data sampled from environments and then leverages this agent to generate novel exploration trajectories. The novel rollouts provide demonstrations with stronger exploration strategies to train a better agent, which in turn produces higher-quality agent demonstrations for the next round of training. We show that this iterative self-improving pipeline readily scales to new environments, and the resulting demonstrations can be transferred across a variety of language-guided navigation tasks, elevating the performance ceiling in diverse goal-oriented navigation tasks. Extensive experiments demonstrate that SID significantly boosts the exploration capabilities and generalization of navigation agents. The resulting agent achieves new state-of-the-art performance on goal-oriented language-guided navigation tasks, including REVERIE, SOON, notably achieving a 50.9% success rate on the unseen validation splits of SOON, surpassing the prior leading approaches by a margin of 13.9%.

Reward-free exploration is a reinforcement learning setting studied by Jin et al. (2020), who address it by running several algorithms with regret guarantees in parallel. In our work, we instead give a more natural adaptive approach for reward-free exploration which directly reduces upper bounds on the maximum MDP estimation error. We show that, interestingly, our reward-free UCRL algorithm can be seen as a variant of an algorithm of Fiechter from 1994, originally proposed for a different objective that we call best-policy identification. We prove that RF-UCRL needs of order ({SAH^4}/{varepsilon^2})(log(1/δ) + S) episodes to output, with probability 1-δ, an varepsilon-approximation of the optimal policy for any reward function. This bound improves over existing sample-complexity bounds in both the small varepsilon and the small δ regimes. We further investigate the relative complexities of reward-free exploration and best-policy identification.

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.

One difficulty in using artificial agents for human-assistive applications lies in the challenge of accurately assisting with a person's goal(s). Existing methods tend to rely on inferring the human's goal, which is challenging when there are many potential goals or when the set of candidate goals is difficult to identify. We propose a new paradigm for assistance by instead increasing the human's ability to control their environment, and formalize this approach by augmenting reinforcement learning with human empowerment. This task-agnostic objective preserves the person's autonomy and ability to achieve any eventual state. We test our approach against assistance based on goal inference, highlighting scenarios where our method overcomes failure modes stemming from goal ambiguity or misspecification. As existing methods for estimating empowerment in continuous domains are computationally hard, precluding its use in real time learned assistance, we also propose an efficient empowerment-inspired proxy metric. Using this, we are able to successfully demonstrate our method in a shared autonomy user study for a challenging simulated teleoperation task with human-in-the-loop training.

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.

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.

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.

Autonomous robots exploring unknown areas face a significant challenge -- navigating effectively without prior maps and with limited external feedback. This challenge intensifies in sparse reward environments, where traditional exploration techniques often fail. In this paper, we introduce TopoNav, a novel framework that empowers robots to overcome these constraints and achieve efficient, adaptable, and goal-oriented exploration. TopoNav's fundamental building blocks are active topological mapping, intrinsic reward mechanisms, and hierarchical objective prioritization. Throughout its exploration, TopoNav constructs a dynamic topological map that captures key locations and pathways. It utilizes intrinsic rewards to guide the robot towards designated sub-goals within this map, fostering structured exploration even in sparse reward settings. To ensure efficient navigation, TopoNav employs the Hierarchical Objective-Driven Active Topologies framework, enabling the robot to prioritize immediate tasks like obstacle avoidance while maintaining focus on the overall goal. We demonstrate TopoNav's effectiveness in simulated environments that replicate real-world conditions. Our results reveal significant improvements in exploration efficiency, navigational accuracy, and adaptability to unforeseen obstacles, showcasing its potential to revolutionize autonomous exploration in a wide range of applications, including search and rescue, environmental monitoring, and planetary exploration.

Offline goal-conditioned reinforcement learning (GCRL) is a promising approach for pretraining generalist policies on large datasets of reward-free trajectories, akin to the self-supervised objectives used to train foundation models for computer vision and natural language processing. However, scaling GCRL to longer horizons remains challenging due to the combination of sparse rewards and discounting, which obscures the comparative advantages of primitive actions with respect to distant goals. Hierarchical RL methods achieve strong empirical results on long-horizon goal-reaching tasks, but their reliance on modular, timescale-specific policies and subgoal generation introduces significant additional complexity and hinders scaling to high-dimensional goal spaces. In this work, we introduce an algorithm to train a flat (non-hierarchical) goal-conditioned policy by bootstrapping on subgoal-conditioned policies with advantage-weighted importance sampling. Our approach eliminates the need for a generative model over the (sub)goal space, which we find is key for scaling to high-dimensional control in large state spaces. We further show that existing hierarchical and bootstrapping-based approaches correspond to specific design choices within our derivation. Across a comprehensive suite of state- and pixel-based locomotion and manipulation benchmarks, our method matches or surpasses state-of-the-art offline GCRL algorithms and scales to complex, long-horizon tasks where prior approaches fail. Project page: https://johnlyzhou.github.io/saw/

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.

In this paper, we propose a general framework for universal zero-shot goal-oriented navigation. Existing zero-shot methods build inference framework upon large language models (LLM) for specific tasks, which differs a lot in overall pipeline and fails to generalize across different types of goal. Towards the aim of universal zero-shot navigation, we propose a uniform graph representation to unify different goals, including object category, instance image and text description. We also convert the observation of agent into an online maintained scene graph. With this consistent scene and goal representation, we preserve most structural information compared with pure text and are able to leverage LLM for explicit graph-based reasoning. Specifically, we conduct graph matching between the scene graph and goal graph at each time instant and propose different strategies to generate long-term goal of exploration according to different matching states. The agent first iteratively searches subgraph of goal when zero-matched. With partial matching, the agent then utilizes coordinate projection and anchor pair alignment to infer the goal location. Finally scene graph correction and goal verification are applied for perfect matching. We also present a blacklist mechanism to enable robust switch between stages. Extensive experiments on several benchmarks show that our UniGoal achieves state-of-the-art zero-shot performance on three studied navigation tasks with a single model, even outperforming task-specific zero-shot methods and supervised universal methods.

In multi-goal Reinforcement Learning, an agent can share experience between related training tasks, resulting in better generalization for new tasks at test time. However, when the goal space has discontinuities and the reward is sparse, a majority of goals are difficult to reach. In this context, a curriculum over goals helps agents learn by adapting training tasks to their current capabilities. In this work we propose Stein Variational Goal Generation (SVGG), which samples goals of intermediate difficulty for the agent, by leveraging a learned predictive model of its goal reaching capabilities. The distribution of goals is modeled with particles that are attracted in areas of appropriate difficulty using Stein Variational Gradient Descent. We show that SVGG outperforms state-of-the-art multi-goal Reinforcement Learning methods in terms of success coverage in hard exploration problems, and demonstrate that it is endowed with a useful recovery property when the environment changes.

Object goal navigation aims to navigate an agent to locations of a given object category in unseen environments. Classical methods explicitly build maps of environments and require extensive engineering while lacking semantic information for object-oriented exploration. On the other hand, end-to-end learning methods alleviate manual map design and predict actions using implicit representations. Such methods, however, lack an explicit notion of geometry and may have limited ability to encode navigation history. In this work, we propose an implicit spatial map for object goal navigation. Our implicit map is recursively updated with new observations at each step using a transformer. To encourage spatial reasoning, we introduce auxiliary tasks and train our model to reconstruct explicit maps as well as to predict visual features, semantic labels and actions. Our method significantly outperforms the state of the art on the challenging MP3D dataset and generalizes well to the HM3D dataset. We successfully deploy our model on a real robot and achieve encouraging object goal navigation results in real scenes using only a few real-world demonstrations. Code, trained models and videos are available at https://www.di.ens.fr/willow/research/onav_rim/.

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.

We present BYOL-Explore, a conceptually simple yet general approach for curiosity-driven exploration in visually-complex environments. BYOL-Explore learns a world representation, the world dynamics, and an exploration policy all-together by optimizing a single prediction loss in the latent space with no additional auxiliary objective. We show that BYOL-Explore is effective in DM-HARD-8, a challenging partially-observable continuous-action hard-exploration benchmark with visually-rich 3-D environments. On this benchmark, we solve the majority of the tasks purely through augmenting the extrinsic reward with BYOL-Explore s intrinsic reward, whereas prior work could only get off the ground with human demonstrations. As further evidence of the generality of BYOL-Explore, we show that it achieves superhuman performance on the ten hardest exploration games in Atari while having a much simpler design than other competitive agents.

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.

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.

The rapid progress of large language models (LLMs) has sparked growing interest in building Artificial General Intelligence (AGI) within Graphical User Interface (GUI) environments. However, existing GUI agents based on LLMs or vision-language models (VLMs) often fail to generalize to novel environments and rely heavily on manually curated, diverse datasets. To overcome these limitations, we introduce ScreenExplorer, a VLM trained via Group Relative Policy Optimization(GRPO) in real, dynamic, and open-ended GUI environments. Innovatively, we introduced a world-model-based curiosity reward function to help the agent overcome the cold-start phase of exploration. Additionally, distilling experience streams further enhances the model's exploration capabilities. Our training framework enhances model exploration in open GUI environments, with trained models showing better environmental adaptation and sustained exploration compared to static deployment models. Our findings offer a scalable pathway toward AGI systems with self-improving capabilities in complex interactive settings.

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.

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).

Reinforcement learning algorithms typically struggle in the absence of a dense, well-shaped reward function. Intrinsically motivated exploration methods address this limitation by rewarding agents for visiting novel states or transitions, but these methods offer limited benefits in large environments where most discovered novelty is irrelevant for downstream tasks. We describe a method that uses background knowledge from text corpora to shape exploration. This method, called ELLM (Exploring with LLMs) rewards an agent for achieving goals suggested by a language model prompted with a description of the agent's current state. By leveraging large-scale language model pretraining, ELLM guides agents toward human-meaningful and plausibly useful behaviors without requiring a human in the loop. We evaluate ELLM in the Crafter game environment and the Housekeep robotic simulator, showing that ELLM-trained agents have better coverage of common-sense behaviors during pretraining and usually match or improve performance on a range of downstream tasks.

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.

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.

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.

Achieving effective test-time scaling requires models to engage in In-Context Exploration -- the intrinsic ability to generate, verify, and refine multiple reasoning hypotheses within a single continuous context. Grounded in State Coverage theory, our analysis identifies a critical bottleneck to enabling this capability: while broader state coverage requires longer reasoning trajectories, the probability of sampling such sequences decays exponentially during autoregressive generation, a phenomenon we term the ``Shallow Exploration Trap''. To bridge this gap, we propose Length-Incentivized Exploration(\method). This simple yet effective recipe explicitly encourages models to explore more via a length-based reward coupled with a redundancy penalty, thereby maximizing state coverage in two-step manner. Comprehensive experiments across different models (Qwen3, Llama) demonstrate that \method effectively incentivize in-context exploration. As a result, our method achieves an average improvement of 4.4\% on in-domain tasks and a 2.7\% gain on out-of-domain benchmarks.

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

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.

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.

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.

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.

Inspired by human conscious planning, we propose Skipper, a model-based reinforcement learning framework utilizing spatio-temporal abstractions to generalize better in novel situations. It automatically decomposes the given task into smaller, more manageable subtasks, and thus enables sparse decision-making and focused computation on the relevant parts of the environment. The decomposition relies on the extraction of an abstracted proxy problem represented as a directed graph, in which vertices and edges are learned end-to-end from hindsight. Our theoretical analyses provide performance guarantees under appropriate assumptions and establish where our approach is expected to be helpful. Generalization-focused experiments validate Skipper's significant advantage in zero-shot generalization, compared to some existing state-of-the-art hierarchical planning methods.

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.

Generative recommendation via autoregressive models has unified retrieval and ranking into a single conditional generation framework. However, fine-tuning these models with Reinforcement Learning (RL) often suffers from a fundamental probability-reward mismatch. Conventional likelihood-dominated decoding (e.g., beam search) exhibits a myopic bias toward locally probable prefixes, which causes two critical failures: (1) insufficient exploration, where high-reward items in low-probability branches are prematurely pruned and rarely sampled, and (2) advantage compression, where trajectories sharing high-probability prefixes receive highly correlated rewards with low within-group variance, yielding a weak comparative signal for RL. To address these challenges, we propose V-STAR, a Value-guided Sampling and Tree-structured Advantage Reinforcement framework. V-STAR forms a self-evolving loop via two synergistic components. First, a Value-Guided Efficient Decoding (VED) is developed to identify decisive nodes and selectively deepen high-potential prefixes. This improves exploration efficiency without exhaustive tree search. Second, we propose Sibling-GRPO, which exploits the induced tree topology to compute sibling-relative advantages and concentrates learning signals on decisive branching decisions. Extensive experiments on both offline and online datasets demonstrate that V-STAR outperforms state-of-the-art baselines, delivering superior accuracy and candidate-set diversity under strict latency constraints.

Reinforcement Learning with Verifiable Rewards (RLVR), particularly GRPO, has become the standard for eliciting LLM reasoning. However, its efficiency in exploration and difficulty adaptation remains an open challenge. In this work, we argue that these bottlenecks stem from an implicit advantage symmetry inherent in Group Relative Advantage Estimation (GRAE). This symmetry induces two critical limitations: (i) at the group level, strict symmetry in weights between correct and incorrect trajectories leaves unsampled action logits unchanged, thereby hindering exploration of novel correct solution. (ii) at the sample level, the algorithm implicitly prioritizes medium-difficulty samples, remaining agnostic to the non-stationary demands of difficulty focus. Through controlled experiments, we reveal that this symmetric property is sub-optimal, yielding two pivotal insights: (i) asymmetrically suppressing the advantages of correct trajectories encourages essential exploration. (ii) learning efficiency is maximized by a curriculum-like transition-prioritizing simpler samples initially before gradually shifting to complex ones. Motivated by these findings, we propose Asymmetric GRAE (A-GRAE), which dynamically modulates exploration incentives and sample-difficulty focus. Experiments across seven benchmarks demonstrate that A-GRAE consistently improves GRPO and its variants across both LLMs and MLLMs.

Humans learn to master open-ended repertoires of skills by imagining and practicing their own goals. This autotelic learning process, literally the pursuit of self-generated (auto) goals (telos), becomes more and more open-ended as the goals become more diverse, abstract and creative. The resulting exploration of the space of possible skills is supported by an inter-individual exploration: goal representations are culturally evolved and transmitted across individuals, in particular using language. Current artificial agents mostly rely on predefined goal representations corresponding to goal spaces that are either bounded (e.g. list of instructions), or unbounded (e.g. the space of possible visual inputs) but are rarely endowed with the ability to reshape their goal representations, to form new abstractions or to imagine creative goals. In this paper, we introduce a language model augmented autotelic agent (LMA3) that leverages a pretrained language model (LM) to support the representation, generation and learning of diverse, abstract, human-relevant goals. The LM is used as an imperfect model of human cultural transmission; an attempt to capture aspects of humans' common-sense, intuitive physics and overall interests. Specifically, it supports three key components of the autotelic architecture: 1)~a relabeler that describes the goals achieved in the agent's trajectories, 2)~a goal generator that suggests new high-level goals along with their decomposition into subgoals the agent already masters, and 3)~reward functions for each of these goals. Without relying on any hand-coded goal representations, reward functions or curriculum, we show that LMA3 agents learn to master a large diversity of skills in a task-agnostic text-based environment.

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.

Intelligent agents progress by continually refining their capabilities through actively exploring environments. Yet robot policies often lack sufficient exploration capability due to action mode collapse. Existing methods that encourage exploration typically rely on random perturbations, which are unsafe and induce unstable, erratic behaviors, thereby limiting their effectiveness. We propose Self-Improvement via On-Manifold Exploration (SOE), a framework that enhances policy exploration and improvement in robotic manipulation. SOE learns a compact latent representation of task-relevant factors and constrains exploration to the manifold of valid actions, ensuring safety, diversity, and effectiveness. It can be seamlessly integrated with arbitrary policy models as a plug-in module, augmenting exploration without degrading the base policy performance. Moreover, the structured latent space enables human-guided exploration, further improving efficiency and controllability. Extensive experiments in both simulation and real-world tasks demonstrate that SOE consistently outperforms prior methods, achieving higher task success rates, smoother and safer exploration, and superior sample efficiency. These results establish on-manifold exploration as a principled approach to sample-efficient policy self-improvement. Project website: https://ericjin2002.github.io/SOE

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.

Open-ended learning benefits immensely from the use of symbolic methods for goal representation as they offer ways to structure knowledge for efficient and transferable learning. However, the existing Hierarchical Reinforcement Learning (HRL) approaches relying on symbolic reasoning are often limited as they require a manual goal representation. The challenge in autonomously discovering a symbolic goal representation is that it must preserve critical information, such as the environment dynamics. In this paper, we propose a developmental mechanism for goal discovery via an emergent representation that abstracts (i.e., groups together) sets of environment states that have similar roles in the task. We introduce a Feudal HRL algorithm that concurrently learns both the goal representation and a hierarchical policy. The algorithm uses symbolic reachability analysis for neural networks to approximate the transition relation among sets of states and to refine the goal representation. We evaluate our approach on complex navigation tasks, showing the learned representation is interpretable, transferrable and results in data efficient learning.

Many popular reinforcement learning problems (e.g., navigation in a maze, some Atari games, mountain car) are instances of the episodic setting under its stochastic shortest path (SSP) formulation, where an agent has to achieve a goal state while minimizing the cumulative cost. Despite the popularity of this setting, the exploration-exploitation dilemma has been sparsely studied in general SSP problems, with most of the theoretical literature focusing on different problems (i.e., fixed-horizon and infinite-horizon) or making the restrictive loop-free SSP assumption (i.e., no state can be visited twice during an episode). In this paper, we study the general SSP problem with no assumption on its dynamics (some policies may actually never reach the goal). We introduce UC-SSP, the first no-regret algorithm in this setting, and prove a regret bound scaling as displaystyle mathcal{O}( D S A D K) after K episodes for any unknown SSP with S states, A actions, positive costs and SSP-diameter D, defined as the smallest expected hitting time from any starting state to the goal. We achieve this result by crafting a novel stopping rule, such that UC-SSP may interrupt the current policy if it is taking too long to achieve the goal and switch to alternative policies that are designed to rapidly terminate the episode.

Robots in many real-world settings have access to force/torque sensors in their gripper and tactile sensing is often necessary in tasks that involve contact-rich motion. In this work, we leverage surprise from mismatches in touch feedback to guide exploration in hard sparse-reward reinforcement learning tasks. Our approach, Touch-based Curiosity (ToC), learns what visible objects interactions are supposed to "feel" like. We encourage exploration by rewarding interactions where the expectation and the experience don't match. In our proposed method, an initial task-independent exploration phase is followed by an on-task learning phase, in which the original interactions are relabeled with on-task rewards. We test our approach on a range of touch-intensive robot arm tasks (e.g. pushing objects, opening doors), which we also release as part of this work. Across multiple experiments in a simulated setting, we demonstrate that our method is able to learn these difficult tasks through sparse reward and curiosity alone. We compare our cross-modal approach to single-modality (touch- or vision-only) approaches as well as other curiosity-based methods and find that our method performs better and is more sample-efficient.

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.

Unsupervised and self-supervised objectives, such as next token prediction, have enabled pre-training generalist models from large amounts of unlabeled data. In reinforcement learning (RL), however, finding a truly general and scalable unsupervised pre-training objective for generalist policies from offline data remains a major open question. While a number of methods have been proposed to enable generic self-supervised RL, based on principles such as goal-conditioned RL, behavioral cloning, and unsupervised skill learning, such methods remain limited in terms of either the diversity of the discovered behaviors, the need for high-quality demonstration data, or the lack of a clear prompting or adaptation mechanism for downstream tasks. In this work, we propose a novel unsupervised framework to pre-train generalist policies that capture diverse, optimal, long-horizon behaviors from unlabeled offline data such that they can be quickly adapted to any arbitrary new tasks in a zero-shot manner. Our key insight is to learn a structured representation that preserves the temporal structure of the underlying environment, and then to span this learned latent space with directional movements, which enables various zero-shot policy "prompting" schemes for downstream tasks. Through our experiments on simulated robotic locomotion and manipulation benchmarks, we show that our unsupervised policies can solve goal-conditioned and general RL tasks in a zero-shot fashion, even often outperforming prior methods designed specifically for each setting. Our code and videos are available at https://seohong.me/projects/hilp/

We propose a hierarchical entity-centric framework for offline Goal-Conditioned Reinforcement Learning (GCRL) that combines subgoal decomposition with factored structure to solve long-horizon tasks in domains with multiple entities. Achieving long-horizon goals in complex environments remains a core challenge in Reinforcement Learning (RL). Domains with multiple entities are particularly difficult due to their combinatorial complexity. GCRL facilitates generalization across goals and the use of subgoal structure, but struggles with high-dimensional observations and combinatorial state-spaces, especially under sparse reward. We employ a two-level hierarchy composed of a value-based GCRL agent and a factored subgoal-generating conditional diffusion model. The RL agent and subgoal generator are trained independently and composed post hoc through selective subgoal generation based on the value function, making the approach modular and compatible with existing GCRL algorithms. We introduce new variations to benchmark tasks that highlight the challenges of multi-entity domains, and show that our method consistently boosts performance of the underlying RL agent on image-based long-horizon tasks with sparse rewards, achieving over 150% higher success rates on the hardest task in our suite and generalizing to increasing horizons and numbers of entities. Rollout videos are provided at: https://sites.google.com/view/hecrl

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 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.

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.

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.

Open-ended learning agents must efficiently prioritize goals in vast possibility spaces, focusing on those that maximize learning progress (LP). When such autotelic exploration is achieved by LLM agents trained with online RL in high-dimensional and evolving goal spaces, a key challenge for LP prediction is modeling one's own competence, a form of metacognitive monitoring. Traditional approaches either require extensive sampling or rely on brittle expert-defined goal groupings. We introduce MAGELLAN, a metacognitive framework that lets LLM agents learn to predict their competence and LP online. By capturing semantic relationships between goals, MAGELLAN enables sample-efficient LP estimation and dynamic adaptation to evolving goal spaces through generalization. In an interactive learning environment, we show that MAGELLAN improves LP prediction efficiency and goal prioritization, being the only method allowing the agent to fully master a large and evolving goal space. These results demonstrate how augmenting LLM agents with a metacognitive ability for LP predictions can effectively scale curriculum learning to open-ended goal spaces.

Generalizable active mapping in complex unknown environments remains a critical challenge for mobile robots. Existing methods, constrained by insufficient training data and conservative exploration strategies, exhibit limited generalizability across scenes with diverse layouts and complex connectivity. To enable scalable training and reliable evaluation, we introduce GLEAM-Bench, the first large-scale benchmark designed for generalizable active mapping with 1,152 diverse 3D scenes from synthetic and real-scan datasets. Building upon this foundation, we propose GLEAM, a unified generalizable exploration policy for active mapping. Its superior generalizability comes mainly from our semantic representations, long-term navigable goals, and randomized strategies. It significantly outperforms state-of-the-art methods, achieving 66.50% coverage (+9.49%) with efficient trajectories and improved mapping accuracy on 128 unseen complex scenes. Project page: https://xiao-chen.tech/gleam/.

Planning with a learned model is arguably a key component of intelligence. There are several challenges in realizing such a component in large-scale reinforcement learning (RL) problems. One such challenge is dealing effectively with continuous action spaces when using tree-search planning (e.g., it is not feasible to consider every action even at just the root node of the tree). In this paper we present a method for selecting affordances useful for planning -- for learning which small number of actions/options from a continuous space of actions/options to consider in the tree-expansion process during planning. We consider affordances that are goal-and-state-conditional mappings to actions/options as well as unconditional affordances that simply select actions/options available in all states. Our selection method is gradient based: we compute gradients through the planning procedure to update the parameters of the function that represents affordances. Our empirical work shows that it is feasible to learn to select both primitive-action and option affordances, and that simultaneously learning to select affordances and planning with a learned value-equivalent model can outperform model-free RL.

Autonomous agents have recently achieved remarkable progress across diverse domains, yet most evaluations focus on short-horizon, fully observable tasks. In contrast, many critical real-world tasks, such as large-scale software development, commercial investment, and scientific discovery, unfold in long-horizon and partially observable scenarios where success hinges on sustained reasoning, planning, memory management, and tool use. Existing benchmarks rarely capture these long-horizon challenges, leaving a gap in systematic evaluation. To bridge this gap, we introduce UltraHorizon a novel benchmark that measures the foundational capabilities essential for complex real-world challenges. We use exploration as a unifying task across three distinct environments to validate these core competencies. Agents are designed in long-horizon discovery tasks where they must iteratively uncover hidden rules through sustained reasoning, planning, memory and tools management, and interaction with environments. Under the heaviest scale setting, trajectories average 200k+ tokens and 400+ tool calls, whereas in standard configurations they still exceed 35k tokens and involve more than 60 tool calls on average. Our extensive experiments reveal that LLM-agents consistently underperform in these settings, whereas human participants achieve higher scores, underscoring a persistent gap in agents' long-horizon abilities. We also observe that simple scaling fails in our task. To better illustrate the failure of agents, we conduct an in-depth analysis of collected trajectories. We identify eight types of errors and attribute them to two primary causes: in-context locking and functional fundamental capability gaps. https://github.com/StarDewXXX/UltraHorizon{Our code will be available here.}

LLM-based agents often operate in a greedy, step-by-step manner, selecting actions solely based on the current observation without considering long-term consequences or alternative paths. This lack of foresight is particularly problematic in web environments, which are only partially observable-limited to browser-visible content (e.g., DOM and UI elements)-where a single misstep often requires complex and brittle navigation to undo. Without an explicit backtracking mechanism, agents struggle to correct errors or systematically explore alternative paths. Tree-search methods provide a principled framework for such structured exploration, but existing approaches lack mechanisms for safe backtracking, making them prone to unintended side effects. They also assume that all actions are reversible, ignoring the presence of irreversible actions-limitations that reduce their effectiveness in realistic web tasks. To address these challenges, we introduce WebOperator, a tree-search framework that enables reliable backtracking and strategic exploration. Our method incorporates a best-first search strategy that ranks actions by both reward estimates and safety considerations, along with a robust backtracking mechanism that verifies the feasibility of previously visited paths before replaying them, preventing unintended side effects. To further guide exploration, WebOperator generates action candidates from multiple, varied reasoning contexts to ensure diverse and robust exploration, and subsequently curates a high-quality action set by filtering out invalid actions pre-execution and merging semantically equivalent ones. Experimental results on WebArena and WebVoyager demonstrate the effectiveness of WebOperator. On WebArena, WebOperator achieves a state-of-the-art 54.6% success rate with gpt-4o, underscoring the critical advantage of integrating strategic foresight with safe execution.

Offline goal-conditioned reinforcement learning (GCRL) aims at solving goal-reaching tasks with sparse rewards from an offline dataset. While prior work has demonstrated various approaches for agents to learn near-optimal policies, these methods encounter limitations when dealing with diverse constraints in complex environments, such as safety constraints. Some of these approaches prioritize goal attainment without considering safety, while others excessively focus on safety at the expense of training efficiency. In this paper, we study the problem of constrained offline GCRL and propose a new method called Recovery-based Supervised Learning (RbSL) to accomplish safety-critical tasks with various goals. To evaluate the method performance, we build a benchmark based on the robot-fetching environment with a randomly positioned obstacle and use expert or random policies to generate an offline dataset. We compare RbSL with three offline GCRL algorithms and one offline safe RL algorithm. As a result, our method outperforms the existing state-of-the-art methods to a large extent. Furthermore, we validate the practicality and effectiveness of RbSL by deploying it on a real Panda manipulator. Code is available at https://github.com/Sunlighted/RbSL.git.

Learning a shared policy that guides the locomotion of different agents is of core interest in Reinforcement Learning (RL), which leads to the study of morphology-agnostic RL. However, existing benchmarks are highly restrictive in the choice of starting point and target point, constraining the movement of the agents within 2D space. In this work, we propose a novel setup for morphology-agnostic RL, dubbed Subequivariant Graph RL in 3D environments (3D-SGRL). Specifically, we first introduce a new set of more practical yet challenging benchmarks in 3D space that allows the agent to have full Degree-of-Freedoms to explore in arbitrary directions starting from arbitrary configurations. Moreover, to optimize the policy over the enlarged state-action space, we propose to inject geometric symmetry, i.e., subequivariance, into the modeling of the policy and Q-function such that the policy can generalize to all directions, improving exploration efficiency. This goal is achieved by a novel SubEquivariant Transformer (SET) that permits expressive message exchange. Finally, we evaluate the proposed method on the proposed benchmarks, where our method consistently and significantly outperforms existing approaches on single-task, multi-task, and zero-shot generalization scenarios. Extensive ablations are also conducted to verify our design. Code and videos are available on our project page: https://alpc91.github.io/SGRL/.

Consider the problem of exploration in sparse-reward or reward-free environments, such as in Montezuma's Revenge. In the curiosity-driven paradigm, the agent is rewarded for how much each realized outcome differs from their predicted outcome. But using predictive error as intrinsic motivation is fragile in stochastic environments, as the agent may become trapped by high-entropy areas of the state-action space, such as a "noisy TV". In this work, we study a natural solution derived from structural causal models of the world: Our key idea is to learn representations of the future that capture precisely the unpredictable aspects of each outcome -- which we use as additional input for predictions, such that intrinsic rewards only reflect the predictable aspects of world dynamics. First, we propose incorporating such hindsight representations into models to disentangle "noise" from "novelty", yielding Curiosity in Hindsight: a simple and scalable generalization of curiosity that is robust to stochasticity. Second, we instantiate this framework for the recently introduced BYOL-Explore algorithm as our prime example, resulting in the noise-robust BYOL-Hindsight. Third, we illustrate its behavior under a variety of different stochasticities in a grid world, and find improvements over BYOL-Explore in hard-exploration Atari games with sticky actions. Notably, we show state-of-the-art results in exploring Montezuma's Revenge with sticky actions, while preserving performance in the non-sticky setting.

Safe navigation is essential for autonomous systems operating in hazardous environments. Traditional planning methods excel at long-horizon tasks but rely on a predefined graph with fixed distance metrics. In contrast, safe Reinforcement Learning (RL) can learn complex behaviors without relying on manual heuristics but fails to solve long-horizon tasks, particularly in goal-conditioned and multi-agent scenarios. In this paper, we introduce a novel method that integrates the strengths of both planning and safe RL. Our method leverages goal-conditioned RL and safe RL to learn a goal-conditioned policy for navigation while concurrently estimating cumulative distance and safety levels using learned value functions via an automated self-training algorithm. By constructing a graph with states from the replay buffer, our method prunes unsafe edges and generates a waypoint-based plan that the agent follows until reaching its goal, effectively balancing faster and safer routes over extended distances. Utilizing this unified high-level graph and a shared low-level goal-conditioned safe RL policy, we extend this approach to address the multi-agent safe navigation problem. In particular, we leverage Conflict-Based Search (CBS) to create waypoint-based plans for multiple agents allowing for their safe navigation over extended horizons. This integration enhances the scalability of goal-conditioned safe RL in multi-agent scenarios, enabling efficient coordination among agents. Extensive benchmarking against state-of-the-art baselines demonstrates the effectiveness of our method in achieving distance goals safely for multiple agents in complex and hazardous environments. Our code and further details about or work is available at https://safe-visual-mapf-mers.csail.mit.edu/.

We investigate an active pure-exploration setting, that includes best-arm identification, in the context of linear stochastic bandits. While asymptotically optimal algorithms exist for standard multi-arm bandits, the existence of such algorithms for the best-arm identification in linear bandits has been elusive despite several attempts to address it. First, we provide a thorough comparison and new insight over different notions of optimality in the linear case, including G-optimality, transductive optimality from optimal experimental design and asymptotic optimality. Second, we design the first asymptotically optimal algorithm for fixed-confidence pure exploration in linear bandits. As a consequence, our algorithm naturally bypasses the pitfall caused by a simple but difficult instance, that most prior algorithms had to be engineered to deal with explicitly. Finally, we avoid the need to fully solve an optimal design problem by providing an approach that entails an efficient implementation.

Unsupervised pre-training strategies have proven to be highly effective in natural language processing and computer vision. Likewise, unsupervised reinforcement learning (RL) holds the promise of discovering a variety of potentially useful behaviors that can accelerate the learning of a wide array of downstream tasks. Previous unsupervised RL approaches have mainly focused on pure exploration and mutual information skill learning. However, despite the previous attempts, making unsupervised RL truly scalable still remains a major open challenge: pure exploration approaches might struggle in complex environments with large state spaces, where covering every possible transition is infeasible, and mutual information skill learning approaches might completely fail to explore the environment due to the lack of incentives. To make unsupervised RL scalable to complex, high-dimensional environments, we propose a novel unsupervised RL objective, which we call Metric-Aware Abstraction (METRA). Our main idea is, instead of directly covering the entire state space, to only cover a compact latent space Z that is metrically connected to the state space S by temporal distances. By learning to move in every direction in the latent space, METRA obtains a tractable set of diverse behaviors that approximately cover the state space, being scalable to high-dimensional environments. Through our experiments in five locomotion and manipulation environments, we demonstrate that METRA can discover a variety of useful behaviors even in complex, pixel-based environments, being the first unsupervised RL method that discovers diverse locomotion behaviors in pixel-based Quadruped and Humanoid. Our code and videos are available at https://seohong.me/projects/metra/

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.

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful paradigm for enhancing the reasoning ability of Large Language Models (LLMs). Yet current RLVR methods often explore poorly, leading to premature convergence and entropy collapse. To address this challenge, we introduce Curiosity-Driven Exploration (CDE), a framework that leverages the model's own intrinsic sense of curiosity to guide exploration. We formalize curiosity with signals from both the actor and the critic: for the actor, we use perplexity over its generated response, and for the critic, we use the variance of value estimates from a multi-head architecture. Both signals serve as an exploration bonus within the RLVR framework to guide the model. Our theoretical analysis shows that the actor-wise bonus inherently penalizes overconfident errors and promotes diversity among correct responses; moreover, we connect the critic-wise bonus to the well-established count-based exploration bonus in RL. Empirically, our method achieves an approximate +3 point improvement over standard RLVR using GRPO/PPO on AIME benchmarks. Further analysis identifies a calibration collapse mechanism within RLVR, shedding light on common LLM failure modes.

Reinforcement learning (RL) in the real world necessitates the development of procedures that enable agents to explore without causing harm to themselves or others. The most successful solutions to the problem of safe RL leverage offline data to learn a safe-set, enabling safe online exploration. However, this approach to safe-learning is often constrained by the demonstrations that are available for learning. In this paper we investigate the influence of the quantity and quality of data used to train the initial safe learning problem offline on the ability to learn safe-RL policies online. Specifically, we focus on tasks with spatially extended goal states where we have few or no demonstrations available. Classically this problem is addressed either by using hand-designed controllers to generate data or by collecting user-generated demonstrations. However, these methods are often expensive and do not scale to more complex tasks and environments. To address this limitation we propose an unsupervised RL-based offline data collection procedure, to learn complex and scalable policies without the need for hand-designed controllers or user demonstrations. Our research demonstrates the significance of providing sufficient demonstrations for agents to learn optimal safe-RL policies online, and as a result, we propose optimistic forgetting, a novel online safe-RL approach that is practical for scenarios with limited data. Further, our unsupervised data collection approach highlights the need to balance diversity and optimality for safe online exploration.

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.

For an autonomous agent to fulfill a wide range of user-specified goals at test time, it must be able to learn broadly applicable and general-purpose skill repertoires. Furthermore, to provide the requisite level of generality, these skills must handle raw sensory input such as images. In this paper, we propose an algorithm that acquires such general-purpose skills by combining unsupervised representation learning and reinforcement learning of goal-conditioned policies. Since the particular goals that might be required at test-time are not known in advance, the agent performs a self-supervised "practice" phase where it imagines goals and attempts to achieve them. We learn a visual representation with three distinct purposes: sampling goals for self-supervised practice, providing a structured transformation of raw sensory inputs, and computing a reward signal for goal reaching. We also propose a retroactive goal relabeling scheme to further improve the sample-efficiency of our method. Our off-policy algorithm is efficient enough to learn policies that operate on raw image observations and goals for a real-world robotic system, and substantially outperforms prior techniques.

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.

We study the problem of learning goal-conditioned policies in Minecraft, a popular, widely accessible yet challenging open-ended environment for developing human-level multi-task agents. We first identify two main challenges of learning such policies: 1) the indistinguishability of tasks from the state distribution, due to the vast scene diversity, and 2) the non-stationary nature of environment dynamics caused by partial observability. To tackle the first challenge, we propose Goal-Sensitive Backbone (GSB) for the policy to encourage the emergence of goal-relevant visual state representations. To tackle the second challenge, the policy is further fueled by an adaptive horizon prediction module that helps alleviate the learning uncertainty brought by the non-stationary dynamics. Experiments on 20 Minecraft tasks show that our method significantly outperforms the best baseline so far; in many of them, we double the performance. Our ablation and exploratory studies then explain how our approach beat the counterparts and also unveil the surprising bonus of zero-shot generalization to new scenes (biomes). We hope our agent could help shed some light on learning goal-conditioned, multi-task agents in challenging, open-ended environments like Minecraft.

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.

Recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) for Large Language Model (LLM) reasoning have been hindered by a persistent challenge: exploration collapse. The semantic homogeneity of random rollouts often traps models in narrow, over-optimized behaviors. While existing methods leverage policy entropy to encourage exploration, they face inherent limitations. Global entropy regularization is susceptible to reward hacking, which can induce meaningless verbosity, whereas local token-selective updates struggle with the strong inductive bias of pre-trained models. To address this, we propose Latent Policy Optimization via Iterative Information Bottleneck (IIB-LPO), a novel approach that shifts exploration from statistical perturbation of token distributions to topological branching of reasoning trajectories. IIB-LPO triggers latent branching at high-entropy states to diversify reasoning paths and employs the Information Bottleneck principle both as a trajectory filter and a self-reward mechanism, ensuring concise and informative exploration. Empirical results across four mathematical reasoning benchmarks demonstrate that IIB-LPO achieves state-of-the-art performance, surpassing prior methods by margins of up to 5.3% in accuracy and 7.4% in diversity metrics.

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

Reinforcement learning (RL) agents often face challenges in balancing exploration and exploitation, particularly in environments where sparse or dense rewards bias learning. Biological systems, such as human toddlers, naturally navigate this balance by transitioning from free exploration with sparse rewards to goal-directed behavior guided by increasingly dense rewards. Inspired by this natural progression, we investigate the Toddler-Inspired Reward Transition in goal-oriented RL tasks. Our study focuses on transitioning from sparse to potential-based dense (S2D) rewards while preserving optimal strategies. Through experiments on dynamic robotic arm manipulation and egocentric 3D navigation tasks, we demonstrate that effective S2D reward transitions significantly enhance learning performance and sample efficiency. Additionally, using a Cross-Density Visualizer, we show that S2D transitions smooth the policy loss landscape, resulting in wider minima that improve generalization in RL models. In addition, we reinterpret Tolman's maze experiments, underscoring the critical role of early free exploratory learning in the context of S2D rewards.

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.

Reinforcement learning with verifiable rewards (RLVR) has recently enhanced the reasoning capabilities of large language models (LLMs), particularly for mathematical problem solving. However, a fundamental limitation remains: as the sampling budget increases, the advantage of RLVR-trained models over their pretrained bases often diminishes or even vanishes, revealing a strong dependence on the base model's restricted search space. We attribute this phenomenon to the widespread use of the reverse Kullback-Leibler (KL) divergence regularizer, whose mode-seeking behavior keeps the policy trapped inside the base model's support region and hampers wider exploration. To address this issue, we propose RAPO (Rewards-Aware Policy Optimization), an algorithm to promote broader yet focused exploration. Our method (i) utilizes the forward KL penalty to replace the reverse KL penalty for out-of-distribution exploration, and (ii) reweights the reference policy to facilitate adaptive in-distribution exploration. We train Qwen2.5-3B and 7B models with RAPO on the 8K SimpleRL-Zero dataset, without supervised fine-tuning, and evaluate them on AIME2024 and AIME2025. Results show that RAPO consistently improves problem-solving performance. Notably, RAPO enables models to surpass the base model's performance ceiling and solves previously intractable problems, advancing the frontier of RLVR for challenging reasoning tasks.

We study the problem of learning in the stochastic shortest path (SSP) setting, where an agent seeks to minimize the expected cost accumulated before reaching a goal state. We design a novel model-based algorithm EB-SSP that carefully skews the empirical transitions and perturbs the empirical costs with an exploration bonus to induce an optimistic SSP problem whose associated value iteration scheme is guaranteed to converge. We prove that EB-SSP achieves the minimax regret rate O(B_{star} S A K), where K is the number of episodes, S is the number of states, A is the number of actions, and B_{star} bounds the expected cumulative cost of the optimal policy from any state, thus closing the gap with the lower bound. Interestingly, EB-SSP obtains this result while being parameter-free, i.e., it does not require any prior knowledge of B_{star}, nor of T_{star}, which bounds the expected time-to-goal of the optimal policy from any state. Furthermore, we illustrate various cases (e.g., positive costs, or general costs when an order-accurate estimate of T_{star} is available) where the regret only contains a logarithmic dependence on T_{star}, thus yielding the first (nearly) horizon-free regret bound beyond the finite-horizon MDP setting.

Autonomous navigation in complex, unstructured outdoor environments requires robots to operate over long ranges without prior maps and limited depth sensing. In such settings, relying solely on geometric frontiers for exploration is often insufficient. In such settings, the ability to reason semantically about where to go and what is safe to traverse is crucial for robust, efficient exploration. This work presents WildOS, a unified system for long-range, open-vocabulary object search that combines safe geometric exploration with semantic visual reasoning. WildOS builds a sparse navigation graph to maintain spatial memory, while utilizing a foundation-model-based vision module, ExploRFM, to score frontier nodes of the graph. ExploRFM simultaneously predicts traversability, visual frontiers, and object similarity in image space, enabling real-time, onboard semantic navigation tasks. The resulting vision-scored graph enables the robot to explore semantically meaningful directions while ensuring geometric safety. Furthermore, we introduce a particle-filter-based method for coarse localization of the open-vocabulary target query, that estimates candidate goal positions beyond the robot's immediate depth horizon, enabling effective planning toward distant goals. Extensive closed-loop field experiments across diverse off-road and urban terrains demonstrate that WildOS enables robust navigation, significantly outperforming purely geometric and purely vision-based baselines in both efficiency and autonomy. Our results highlight the potential of vision foundation models to drive open-world robotic behaviors that are both semantically informed and geometrically grounded. Project Page: https://leggedrobotics.github.io/wildos/

Effectively scaling GUI automation is essential for computer-use agents (CUAs); however, existing work primarily focuses on scaling GUI grounding rather than the more crucial GUI planning, which requires more sophisticated data collection. In reality, the exploration process of a CUA across apps/desktops/web pages typically follows a tree structure, with earlier functional entry points often being explored more frequently. Thus, organizing large-scale trajectories into tree structures can reduce data cost and streamline the data scaling of GUI planning. In this work, we propose TreeCUA to efficiently scale GUI automation with tree-structured verifiable evolution. We propose a multi-agent collaborative framework to explore the environment, verify actions, summarize trajectories, and evaluate quality to generate high-quality and scalable GUI trajectories. To improve efficiency, we devise a novel tree-based topology to store and replay duplicate exploration nodes, and design an adaptive exploration algorithm to balance the depth (i.e., trajectory difficulty) and breadth (i.e., trajectory diversity). Moreover, we develop world knowledge guidance and global memory backtracking to avoid low-quality generation. Finally, we naturally extend and propose the TreeCUA-DPO method from abundant tree node information, improving GUI planning capability by referring to the branch information of adjacent trajectories. Experimental results show that TreeCUA and TreeCUA-DPO offer significant improvements, and out-of-domain (OOD) studies further demonstrate strong generalization. All trajectory node information and code will be available at https://github.com/UITron-hub/TreeCUA.

Reinforcement learning with verifiable rewards (RLVR) has shown great promise in enhancing the reasoning abilities of large reasoning models (LRMs). However, it suffers from a critical issue: entropy collapse and premature convergence. Naive entropy regularization, a common approach for encouraging exploration in the traditional RL literature, fails to address this problem in the context of LRM. Our analysis reveals that this failure stems from the vast action space and long trajectories in LRMs, which easily trigger a global entropy explosion as the model indiscriminately explores all possible actions and states. To address this, we propose SIREN (SelectIve entRopy rEgularizatioN), a method that confines exploration to a meaningful subset of actions and states. SIREN achieves this through a two-step entropy masking mechanism, consisting of a top-p mask and a peak-entropy mask. In addition, regularization is transformed into a self-anchored form to stabilize training. Across five mathematical benchmarks, SIREN attains superior average performance over previous entropy-related RLVR approaches, exemplified by a +6.6 maj@k improvement on AIME24/25 with Qwen2.5-Math-7B. Further analysis confirms that SIREN promotes greater response diversity and maintains entropy at an appropriate level, which helps to preserve the validation pass@k throughout training. This effectively mitigates the premature convergence problem common in RLVR for LRM.

With the flourishing development of intelligent warehousing systems, the technology of Automated Guided Vehicle (AGV) has experienced rapid growth. Within intelligent warehousing environments, AGV is required to safely and rapidly plan an optimal path in complex and dynamic environments. Most research has studied deep reinforcement learning to address this challenge. However, in the environments with sparse extrinsic rewards, these algorithms often converge slowly, learn inefficiently or fail to reach the target. Random Network Distillation (RND), as an exploration enhancement, can effectively improve the performance of proximal policy optimization, especially enhancing the additional intrinsic rewards of the AGV agent which is in sparse reward environments. Moreover, most of the current research continues to use 2D grid mazes as experimental environments. These environments have insufficient complexity and limited action sets. To solve this limitation, we present simulation environments of AGV path planning with continuous actions and positions for AGVs, so that it can be close to realistic physical scenarios. Based on our experiments and comprehensive analysis of the proposed method, the results demonstrate that our proposed method enables AGV to more rapidly complete path planning tasks with continuous actions in our environments. A video of part of our experiments can be found at https://youtu.be/lwrY9YesGmw.

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.

In image-based robot manipulation tasks with large observation and action spaces, reinforcement learning struggles with low sample efficiency, slow training speed, and uncertain convergence. As an alternative, large pre-trained foundation models have shown promise in robotic manipulation, particularly in zero-shot and few-shot applications. However, using these models directly is unreliable due to limited reasoning capabilities and challenges in understanding physical and spatial contexts. This paper introduces ExploRLLM, a novel approach that leverages the inductive bias of foundation models (e.g. Large Language Models) to guide exploration in reinforcement learning. We also exploit these foundation models to reformulate the action and observation spaces to enhance the training efficiency in reinforcement learning. Our experiments demonstrate that guided exploration enables much quicker convergence than training without it. Additionally, we validate that ExploRLLM outperforms vanilla foundation model baselines and that the policy trained in simulation can be applied in real-world settings without additional training.

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.

Understanding an agent's goals helps explain and predict its behaviour, yet there is no established methodology for reliably attributing goals to agentic systems. We propose a framework for evaluating goal-directedness that integrates behavioural evaluation with interpretability-based analyses of models' internal representations. As a case study, we examine an LLM agent navigating a 2D grid world toward a goal state. Behaviourally, we evaluate the agent against an optimal policy across varying grid sizes, obstacle densities, and goal structures, finding that performance scales with task difficulty while remaining robust to difficulty-preserving transformations and complex goal structures. We then use probing methods to decode the agent's internal representations of the environment state and its multi-step action plans. We find that the LLM agent non-linearly encodes a coarse spatial map of the environment, preserving approximate task-relevant cues about its position and the goal location; that its actions are broadly consistent with these internal representations; and that reasoning reorganises them, shifting from broader environment structural cues toward information supporting immediate action selection. Our findings support the view that introspective examination is required beyond behavioural evaluations to characterise how agents represent and pursue their objectives.

Reinforcement learning struggles in the face of long-horizon tasks and sparse goals due to the difficulty in manual reward specification. While existing methods address this by adding intrinsic rewards, they may fail to provide meaningful guidance in long-horizon decision-making tasks with large state and action spaces, lacking purposeful exploration. Inspired by human cognition, we propose a new multi-modal model-based RL approach named Dreaming with Large Language Models (DLLM). DLLM integrates the proposed hinting subgoals from the LLMs into the model rollouts to encourage goal discovery and reaching in challenging tasks. By assigning higher intrinsic rewards to samples that align with the hints outlined by the language model during model rollouts, DLLM guides the agent toward meaningful and efficient exploration. Extensive experiments demonstrate that the DLLM outperforms recent methods in various challenging, sparse-reward environments such as HomeGrid, Crafter, and Minecraft by 27.7\%, 21.1\%, and 9.9\%, respectively.

Image-goal navigation aims to steer an agent towards the goal location specified by an image. Most prior methods tackle this task by learning a navigation policy, which extracts visual features of goal and observation images, compares their similarity and predicts actions. However, if the agent is in a different room from the goal image, it's extremely challenging to identify their similarity and infer the likely goal location, which may result in the agent wandering around. Intuitively, when humans carry out this task, they may roughly compare the current observation with the goal image, having an approximate concept of whether they are in the same room before executing the actions. Inspired by this intuition, we try to imitate human behaviour and propose a Room Expert Guided Image-Goal Navigation model (REGNav) to equip the agent with the ability to analyze whether goal and observation images are taken in the same room. Specifically, we first pre-train a room expert with an unsupervised learning technique on the self-collected unlabelled room images. The expert can extract the hidden room style information of goal and observation images and predict their relationship about whether they belong to the same room. In addition, two different fusion approaches are explored to efficiently guide the agent navigation with the room relation knowledge. Extensive experiments show that our REGNav surpasses prior state-of-the-art works on three popular benchmarks.

Offline goal-conditioned RL (GCRL) offers a way to train general-purpose agents from fully offline datasets. In addition to being conservative within the dataset, the generalization ability to achieve unseen goals is another fundamental challenge for offline GCRL. However, to the best of our knowledge, this problem has not been well studied yet. In this paper, we study out-of-distribution (OOD) generalization of offline GCRL both theoretically and empirically to identify factors that are important. In a number of experiments, we observe that weighted imitation learning enjoys better generalization than pessimism-based offline RL method. Based on this insight, we derive a theory for OOD generalization, which characterizes several important design choices. We then propose a new offline GCRL method, Generalizable Offline goAl-condiTioned RL (GOAT), by combining the findings from our theoretical and empirical studies. On a new benchmark containing 9 independent identically distributed (IID) tasks and 17 OOD tasks, GOAT outperforms current state-of-the-art methods by a large margin.

In this work, from a theoretical lens, we aim to understand why large language model (LLM) empowered agents are able to solve decision-making problems in the physical world. To this end, consider a hierarchical reinforcement learning (RL) model where the LLM Planner and the Actor perform high-level task planning and low-level execution, respectively. Under this model, the LLM Planner navigates a partially observable Markov decision process (POMDP) by iteratively generating language-based subgoals via prompting. Under proper assumptions on the pretraining data, we prove that the pretrained LLM Planner effectively performs Bayesian aggregated imitation learning (BAIL) through in-context learning. Additionally, we highlight the necessity for exploration beyond the subgoals derived from BAIL by proving that naively executing the subgoals returned by LLM leads to a linear regret. As a remedy, we introduce an ε-greedy exploration strategy to BAIL, which is proven to incur sublinear regret when the pretraining error is small. Finally, we extend our theoretical framework to include scenarios where the LLM Planner serves as a world model for inferring the transition model of the environment and to multi-agent settings, enabling coordination among multiple Actors.

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.

Today's AI systems have human-designed, fixed architectures and cannot autonomously and continuously improve themselves. The advance of AI could itself be automated. If done safely, that would accelerate AI development and allow us to reap its benefits much sooner. Meta-learning can automate the discovery of novel algorithms, but is limited by first-order improvements and the human design of a suitable search space. The G\"odel machine proposed a theoretical alternative: a self-improving AI that repeatedly modifies itself in a provably beneficial manner. Unfortunately, proving that most changes are net beneficial is impossible in practice. We introduce the Darwin G\"odel Machine (DGM), a self-improving system that iteratively modifies its own code (thereby also improving its ability to modify its own codebase) and empirically validates each change using coding benchmarks. Inspired by Darwinian evolution and open-endedness research, the DGM maintains an archive of generated coding agents. It grows the archive by sampling an agent from it and using a foundation model to create a new, interesting, version of the sampled agent. This open-ended exploration forms a growing tree of diverse, high-quality agents and allows the parallel exploration of many different paths through the search space. Empirically, the DGM automatically improves its coding capabilities (e.g., better code editing tools, long-context window management, peer-review mechanisms), increasing performance on SWE-bench from 20.0% to 50.0%, and on Polyglot from 14.2% to 30.7%. Furthermore, the DGM significantly outperforms baselines without self-improvement or open-ended exploration. All experiments were done with safety precautions (e.g., sandboxing, human oversight). The DGM is a significant step toward self-improving AI, capable of gathering its own stepping stones along paths that unfold into endless innovation.

Navigation in unfamiliar environments presents a major challenge for robots: while mapping and planning techniques can be used to build up a representation of the world, quickly discovering a path to a desired goal in unfamiliar settings with such methods often requires lengthy mapping and exploration. Humans can rapidly navigate new environments, particularly indoor environments that are laid out logically, by leveraging semantics -- e.g., a kitchen often adjoins a living room, an exit sign indicates the way out, and so forth. Language models can provide robots with such knowledge, but directly using language models to instruct a robot how to reach some destination can also be impractical: while language models might produce a narrative about how to reach some goal, because they are not grounded in real-world observations, this narrative might be arbitrarily wrong. Therefore, in this paper we study how the ``semantic guesswork'' produced by language models can be utilized as a guiding heuristic for planning algorithms. Our method, Language Frontier Guide (LFG), uses the language model to bias exploration of novel real-world environments by incorporating the semantic knowledge stored in language models as a search heuristic for planning with either topological or metric maps. We evaluate LFG in challenging real-world environments and simulated benchmarks, outperforming uninformed exploration and other ways of using language models.

Reinforcement Learning from Verifiable Rewards (RLVR) improves the reasoning abilities of Large Language Models (LLMs) but it struggles with unstable exploration. We propose FR3E (First Return, Entropy-Eliciting Explore), a structured exploration framework that identifies high-uncertainty decision points in reasoning trajectories and performs targeted rollouts to construct semantically grounded intermediate feedback. Our method provides targeted guidance without relying on dense supervision. Empirical results on mathematical reasoning benchmarks(AIME24) show that FR3E promotes more stable training, produces longer and more coherent responses, and increases the proportion of fully correct trajectories. These results highlight the framework's effectiveness in improving LLM reasoning through more robust and structured exploration.

We present LGX, a novel algorithm for Object Goal Navigation in a "language-driven, zero-shot manner", where an embodied agent navigates to an arbitrarily described target object in a previously unexplored environment. Our approach leverages the capabilities of Large Language Models (LLMs) for making navigational decisions by mapping the LLMs implicit knowledge about the semantic context of the environment into sequential inputs for robot motion planning. Simultaneously, we also conduct generalized target object detection using a pre-trained Vision-Language grounding model. We achieve state-of-the-art zero-shot object navigation results on RoboTHOR with a success rate (SR) improvement of over 27% over the current baseline of the OWL-ViT CLIP on Wheels (OWL CoW). Furthermore, we study the usage of LLMs for robot navigation and present an analysis of the various semantic factors affecting model output. Finally, we showcase the benefits of our approach via real-world experiments that indicate the superior performance of LGX when navigating to and detecting visually unique objects.

We evaluate language models on their ability to explore interactive environments under a limited interaction budget. We introduce three parametric tasks with controllable exploration difficulty, spanning continuous and discrete environments. Across state-of-the-art models, we find systematic under-exploration and suboptimal solutions, with performance often significantly worse than simple explore--exploit heuristic baselines and scaling weakly as the budget increases. Finally, we study two lightweight interventions: splitting a fixed budget into parallel executions, which surprisingly improves performance despite a no-gain theoretical result for our tasks, and periodically summarizing the interaction history, which preserves key discoveries and further improves exploration.

Offline Goal-Conditioned Reinforcement Learning (GCRL) is tasked with learning to achieve multiple goals in an environment purely from offline datasets using sparse reward functions. Offline GCRL is pivotal for developing generalist agents capable of leveraging pre-existing datasets to learn diverse and reusable skills without hand-engineering reward functions. However, contemporary approaches to GCRL based on supervised learning and contrastive learning are often suboptimal in the offline setting. An alternative perspective on GCRL optimizes for occupancy matching, but necessitates learning a discriminator, which subsequently serves as a pseudo-reward for downstream RL. Inaccuracies in the learned discriminator can cascade, negatively influencing the resulting policy. We present a novel approach to GCRL under a new lens of mixture-distribution matching, leading to our discriminator-free method: SMORe. The key insight is combining the occupancy matching perspective of GCRL with a convex dual formulation to derive a learning objective that can better leverage suboptimal offline data. SMORe learns scores or unnormalized densities representing the importance of taking an action at a state for reaching a particular goal. SMORe is principled and our extensive experiments on the fully offline GCRL benchmark composed of robot manipulation and locomotion tasks, including high-dimensional observations, show that SMORe can outperform state-of-the-art baselines by a significant margin.

In many real-world scenarios, rewards extrinsic to the agent are extremely sparse, or absent altogether. In such cases, curiosity can serve as an intrinsic reward signal to enable the agent to explore its environment and learn skills that might be useful later in its life. We formulate curiosity as the error in an agent's ability to predict the consequence of its own actions in a visual feature space learned by a self-supervised inverse dynamics model. Our formulation scales to high-dimensional continuous state spaces like images, bypasses the difficulties of directly predicting pixels, and, critically, ignores the aspects of the environment that cannot affect the agent. The proposed approach is evaluated in two environments: VizDoom and Super Mario Bros. Three broad settings are investigated: 1) sparse extrinsic reward, where curiosity allows for far fewer interactions with the environment to reach the goal; 2) exploration with no extrinsic reward, where curiosity pushes the agent to explore more efficiently; and 3) generalization to unseen scenarios (e.g. new levels of the same game) where the knowledge gained from earlier experience helps the agent explore new places much faster than starting from scratch. Demo video and code available at https://pathak22.github.io/noreward-rl/

Intelligent agents need to select long sequences of actions to solve complex tasks. While humans easily break down tasks into subgoals and reach them through millions of muscle commands, current artificial intelligence is limited to tasks with horizons of a few hundred decisions, despite large compute budgets. Research on hierarchical reinforcement learning aims to overcome this limitation but has proven to be challenging, current methods rely on manually specified goal spaces or subtasks, and no general solution exists. We introduce Director, a practical method for learning hierarchical behaviors directly from pixels by planning inside the latent space of a learned world model. The high-level policy maximizes task and exploration rewards by selecting latent goals and the low-level policy learns to achieve the goals. Despite operating in latent space, the decisions are interpretable because the world model can decode goals into images for visualization. Director outperforms exploration methods on tasks with sparse rewards, including 3D maze traversal with a quadruped robot from an egocentric camera and proprioception, without access to the global position or top-down view that was used by prior work. Director also learns successful behaviors across a wide range of environments, including visual control, Atari games, and DMLab levels.

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.

Reinforcement learning has empowered large language models to act as intelligent agents, yet training them for long-horizon tasks remains challenging due to the scarcity of high-quality trajectories, especially under limited resources. Existing methods typically scale up rollout sizes and indiscriminately allocate computational resources among intermediate steps. Such attempts inherently waste substantial computation budget on trivial steps while failing to guarantee sample quality. To address this, we propose Spark (Strategic Policy-Aware exploRation via Key-state dynamic branching), a novel framework that selectively branches at critical decision states for resource-efficient exploration. Our key insight is to activate adaptive branching exploration at critical decision points to probe promising trajectories, thereby achieving precise resource allocation that prioritizes sampling quality over blind coverage. This design leverages the agent's intrinsic decision-making signals to reduce dependence on human priors, enabling the agent to autonomously expand exploration and achieve stronger generalization. Experiments across diverse tasks (e.g., embodied planning), demonstrate that Spark achieves superior success rates with significantly fewer training samples, exhibiting robust generalization even in unseen scenarios.

Information sharing is critical in time-sensitive and realistic multi-robot exploration, especially for smaller robotic teams in large-scale environments where connectivity may be sparse and intermittent. Existing methods often overlook such communication constraints by assuming unrealistic global connectivity. Other works account for communication constraints (by maintaining close proximity or line of sight during information exchange), but are often inefficient. For instance, preplanned rendezvous approaches typically involve unnecessary detours resulting from poorly timed rendezvous, while pursuit-based approaches often result in short-sighted decisions due to their greedy nature. We present IR2, a deep reinforcement learning approach to information sharing for multi-robot exploration. Leveraging attention-based neural networks trained via reinforcement and curriculum learning, IR2 allows robots to effectively reason about the longer-term trade-offs between disconnecting for solo exploration and reconnecting for information sharing. In addition, we propose a hierarchical graph formulation to maintain a sparse yet informative graph, enabling our approach to scale to large-scale environments. We present simulation results in three large-scale Gazebo environments, which show that our approach yields 6.6-34.1% shorter exploration paths when compared to state-of-the-art baselines, and lastly deploy our learned policy on hardware. Our simulation training and testing code is available at https://ir2-explore.github.io.

Hierarchical reinforcement learning has been a compelling approach for achieving goal directed behavior over long sequences of actions. However, it has been challenging to implement in realistic or open-ended environments. A main challenge has been to find the right space of sub-goals over which to instantiate a hierarchy. We present a novel approach where we use data from humans solving these tasks to softly supervise the goal space for a set of long range tasks in a 3D embodied environment. In particular, we use unconstrained natural language to parameterize this space. This has two advantages: first, it is easy to generate this data from naive human participants; second, it is flexible enough to represent a vast range of sub-goals in human-relevant tasks. Our approach outperforms agents that clone expert behavior on these tasks, as well as HRL from scratch without this supervised sub-goal space. Our work presents a novel approach to combining human expert supervision with the benefits and flexibility of reinforcement learning.

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.

Reinforcement learning has become essential for strengthening the reasoning abilities of large language models, yet current exploration mechanisms remain fundamentally misaligned with how these models actually learn. Entropy bonuses and external semantic comparators encourage surface level variation but offer no guarantee that sampled trajectories differ in the update directions that shape optimization. We propose G2RL, a gradient guided reinforcement learning framework in which exploration is driven not by external heuristics but by the model own first order update geometry. For each response, G2RL constructs a sequence level feature from the model final layer sensitivity, obtainable at negligible cost from a standard forward pass, and measures how each trajectory would reshape the policy by comparing these features within a sampled group. Trajectories that introduce novel gradient directions receive a bounded multiplicative reward scaler, while redundant or off manifold updates are deemphasized, yielding a self referential exploration signal that is naturally aligned with PPO style stability and KL control. Across math and general reasoning benchmarks (MATH500, AMC, AIME24, AIME25, GPQA, MMLUpro) on Qwen3 base 1.7B and 4B models, G2RL consistently improves pass@1, maj@16, and pass@k over entropy based GRPO and external embedding methods. Analyzing the induced geometry, we find that G2RL expands exploration into substantially more orthogonal and often opposing gradient directions while maintaining semantic coherence, revealing that a policy own update space provides a far more faithful and effective basis for guiding exploration in large language model reinforcement learning.

Active Visual Exploration (AVE) is a task that involves dynamically selecting observations (glimpses), which is critical to facilitate comprehension and navigation within an environment. While modern AVE methods have demonstrated impressive performance, they are constrained to fixed-scale glimpses from rigid grids. In contrast, existing mobile platforms equipped with optical zoom capabilities can capture glimpses of arbitrary positions and scales. To address this gap between software and hardware capabilities, we introduce AdaGlimpse. It uses Soft Actor-Critic, a reinforcement learning algorithm tailored for exploration tasks, to select glimpses of arbitrary position and scale. This approach enables our model to rapidly establish a general awareness of the environment before zooming in for detailed analysis. Experimental results demonstrate that AdaGlimpse surpasses previous methods across various visual tasks while maintaining greater applicability in realistic AVE scenarios.

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.

Reinforcement learning (RL) in long horizon and sparse reward tasks is notoriously difficult and requires a lot of training steps. A standard solution to speed up the process is to leverage additional reward signals, shaping it to better guide the learning process. In the context of language-conditioned RL, the abstraction and generalisation properties of the language input provide opportunities for more efficient ways of shaping the reward. In this paper, we leverage this idea and propose an automated reward shaping method where the agent extracts auxiliary objectives from the general language goal. These auxiliary objectives use a question generation (QG) and question answering (QA) system: they consist of questions leading the agent to try to reconstruct partial information about the global goal using its own trajectory. When it succeeds, it receives an intrinsic reward proportional to its confidence in its answer. This incentivizes the agent to generate trajectories which unambiguously explain various aspects of the general language goal. Our experimental study shows that this approach, which does not require engineer intervention to design the auxiliary objectives, improves sample efficiency by effectively directing exploration.

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.

Visual navigation with an image as goal is a fundamental and challenging problem. Conventional methods either rely on end-to-end RL learning or modular-based policy with topological graph or BEV map as memory, which cannot fully model the geometric relationship between the explored 3D environment and the goal image. In order to efficiently and accurately localize the goal image in 3D space, we build our navigation system upon the renderable 3D gaussian (3DGS) representation. However, due to the computational intensity of 3DGS optimization and the large search space of 6-DoF camera pose, directly leveraging 3DGS for image localization during agent exploration process is prohibitively inefficient. To this end, we propose IGL-Nav, an Incremental 3D Gaussian Localization framework for efficient and 3D-aware image-goal navigation. Specifically, we incrementally update the scene representation as new images arrive with feed-forward monocular prediction. Then we coarsely localize the goal by leveraging the geometric information for discrete space matching, which can be equivalent to efficient 3D convolution. When the agent is close to the goal, we finally solve the fine target pose with optimization via differentiable rendering. The proposed IGL-Nav outperforms existing state-of-the-art methods by a large margin across diverse experimental configurations. It can also handle the more challenging free-view image-goal setting and be deployed on real-world robotic platform using a cellphone to capture goal image at arbitrary pose. Project page: https://gwxuan.github.io/IGL-Nav/.

Embodied agents equipped with GPT as their brain have exhibited extraordinary thinking and decision-making abilities across various tasks. However, existing zero-shot agents for vision-and-language navigation (VLN) only prompt the GPT to handle excessive environmental information and select potential locations within localized environments, without constructing an effective ''global-view'' (e.g., a commonly-used map) for the agent to understand the overall environment. In this work, we present a novel map-guided GPT-based path-planning agent, dubbed MapGPT, for the zero-shot VLN task. Specifically, we convert a topological map constructed online into prompts to encourage map-guided global exploration, and require the agent to explicitly output and update multi-step path planning to avoid getting stuck in local exploration. Extensive experiments demonstrate that our MapGPT is effective, achieving impressive performance on both the R2R and REVERIE datasets (38.8% and 28.4% success rate, respectively) and showcasing the newly emerged global thinking and path planning capabilities of the GPT model. Unlike previous VLN agents, which require separate parameters fine-tuning or specific prompt design to accommodate various instruction styles across different datasets, our MapGPT is more unified as it can adapt to different instruction styles seamlessly, which is the first of its kind in this field.

Offline reinforcement learning (RL) provides a promising solution to learning an agent fully relying on a data-driven paradigm. However, constrained by the limited quality of the offline dataset, its performance is often sub-optimal. Therefore, it is desired to further finetune the agent via extra online interactions before deployment. Unfortunately, offline-to-online RL can be challenging due to two main challenges: constrained exploratory behavior and state-action distribution shift. To this end, we propose a Simple Unified uNcertainty-Guided (SUNG) framework, which naturally unifies the solution to both challenges with the tool of uncertainty. Specifically, SUNG quantifies uncertainty via a VAE-based state-action visitation density estimator. To facilitate efficient exploration, SUNG presents a practical optimistic exploration strategy to select informative actions with both high value and high uncertainty. Moreover, SUNG develops an adaptive exploitation method by applying conservative offline RL objectives to high-uncertainty samples and standard online RL objectives to low-uncertainty samples to smoothly bridge offline and online stages. SUNG achieves state-of-the-art online finetuning performance when combined with different offline RL methods, across various environments and datasets in D4RL benchmark.

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.

Exploration is essential for solving complex Reinforcement Learning (RL) tasks. Maximum State-Visitation Entropy (MSVE) formulates the exploration problem as a well-defined policy optimization problem whose solution aims at visiting all states as uniformly as possible. This is in contrast to standard uncertainty-based approaches where exploration is transient and eventually vanishes. However, existing approaches to MSVE are theoretically justified only for discrete state-spaces as they are oblivious to the geometry of continuous domains. We address this challenge by introducing Geometric Entropy Maximisation (GEM), a new algorithm that maximises the geometry-aware Shannon entropy of state-visits in both discrete and continuous domains. Our key theoretical contribution is casting geometry-aware MSVE exploration as a tractable problem of optimising a simple and novel noise-contrastive objective function. In our experiments, we show the efficiency of GEM in solving several RL problems with sparse rewards, compared against other deep RL exploration approaches.

What drives exploration? Understanding intrinsic motivation is a long-standing challenge in both cognitive science and artificial intelligence; numerous objectives have been proposed and used to train agents, yet there remains a gap between human and agent exploration. We directly compare adults, children, and AI agents in a complex open-ended environment, Crafter, and study how common intrinsic objectives: Entropy, Information Gain, and Empowerment, relate to their behavior. We find that only Entropy and Empowerment are consistently positively correlated with human exploration progress, indicating that these objectives may better inform intrinsic reward design for agents. Furthermore, across agents and humans we observe that Entropy initially increases rapidly, then plateaus, while Empowerment increases continuously, suggesting that state diversity may provide more signal in early exploration, while advanced exploration should prioritize control. Finally, we find preliminary evidence that private speech utterances, and particularly goal verbalizations, may aid exploration in children. Our data is available at https://github.com/alyd/humans_in_crafter_data.

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

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.

This work advances autonomous robot exploration by integrating agent-level semantic reasoning with fast local control. We introduce FARE, a hierarchical autonomous exploration framework that integrates a large language model (LLM) for global reasoning with a reinforcement learning (RL) policy for local decision making. FARE follows a fast-slow thinking paradigm. The slow-thinking LLM module interprets a concise textual description of the unknown environment and synthesizes an agent-level exploration strategy, which is then grounded into a sequence of global waypoints through a topological graph. To further improve reasoning efficiency, this module employs a modularity-based pruning mechanism that reduces redundant graph structures. The fast-thinking RL module executes exploration by reacting to local observations while being guided by the LLM-generated global waypoints. The RL policy is additionally shaped by a reward term that encourages adherence to the global waypoints, enabling coherent and robust closed-loop behavior. This architecture decouples semantic reasoning from geometric decision, allowing each module to operate in its appropriate temporal and spatial scale. In challenging simulated environments, our results show that FARE achieves substantial improvements in exploration efficiency over state-of-the-art baselines. We further deploy FARE on hardware and validate it in complex, large scale 200mtimes130m building environment.