RL Exploration

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.

Many robotic control tasks require policies to act on orientations, yet the geometry of SO(3) makes this nontrivial. Because SO(3) admits no global, smooth, minimal parameterization, common representations such as Euler angles, quaternions, rotation matrices, and Lie algebra coordinates introduce distinct constraints and failure modes. While these trade-offs are well studied for supervised learning, their implications for actions in reinforcement learning remain unclear. We systematically evaluate SO(3) action representations across three standard continuous control algorithms, PPO, SAC, and TD3, under dense and sparse rewards. We compare how representations shape exploration, interact with entropy regularization, and affect training stability through empirical studies and analyze the implications of different projections for obtaining valid rotations from Euclidean network outputs. Across a suite of robotics benchmarks, we quantify the practical impact of these choices and distill simple, implementation-ready guidelines for selecting and using rotation actions. Our results highlight that representation-induced geometry strongly influences exploration and optimization and show that representing actions as tangent vectors in the local frame yields the most reliable results across algorithms. The project webpage and code are available at amacati.github.io/so3_primer.

Reinforcement Learning with Verifiable Rewards (RLVR) has become a widely adopted technique for enhancing the reasoning ability of Large Language Models (LLMs). However, the effectiveness of RLVR strongly depends on the capability of base models. This issue arises because it requires the model to have sufficient capability to perform high-quality exploration, which involves both effectiveness and diversity. Unfortunately, existing methods address this issue by imitating expert trajectories, which improve effectiveness but neglect diversity. To address this, we argue that the expert only needs to provide guidance only at critical decision points rather than the entire reasoning path. Based on this insight, we propose MENTOR: Mixed-policy Expert Navigation for Token-level Optimization of Reasoning, a framework that provides expert guidance only at critical decision points to perform effective and diverse exploration in RLVR. Extensive experiments show that MENTOR enables models capture the essence of expert strategies rather than surface imitation, thereby performing high-quality exploration and achieving superior overall performance. Our code is available online.

For groups of autonomous agents to achieve a particular goal, they must engage in coordination and long-horizon reasoning. Rather than relying on complex reward functions and explicit cooperation mechanisms, we ask what minimal ingredients are required for effective coordination and exploration to emerge in multi-agent settings. We investigate this question through self-supervised goal-reaching, where agents aim to maximize the likelihood of visiting a goal state rather than maximizing a reward. Despite a sparse feedback signal, we present empirical results that show self-supervised goal-reaching techniques enable agents to learn from such feedback. On MARL benchmarks, self-supervised goal-reaching outperforms alternative approaches that have access to the same sparse reward signal. Furthermore, we empirically demonstrate that multi-agent self-supervised goal-reaching approaches can be more robust than single-agent strategies. While there is no explicit exploration mechanism, this approach explores nontrivial intermediate coordination strategies in sparse settings where alternative approaches fail to achieve a single success.

Multi-agent reinforcement learning (MARL) methods have achieved state-of-the-art results on a range of multi-agent tasks. Yet, MARL algorithms typically require significantly more environment interactions than their single-agent counterparts to converge, a problem exacerbated by the difficulty in exploring over a large joint action space and the high variance intrinsic to MARL environments. To tackle these issues, we propose a novel algorithm that combines a decomposed centralized critic with decentralized ensemble learning, incorporating several key contributions. The main component in our scheme is a selective exploration method that leverages ensemble kurtosis. We extend the global decomposed critic with a diversity-regularized ensemble of individual critics and utilize its excess kurtosis to guide exploration toward high-uncertainty states and actions. To improve sample efficiency, we train the centralized critic with a novel truncated variation of the TD($λ$) algorithm, enabling efficient off-policy learning with reduced variance. On the actor side, our suggested algorithm adapts the mixed samples approach to MARL, mixing on-policy and off-policy loss functions for training the actors. This approach balances between stability and efficiency and outperforms purely off-policy learning. The evaluation shows our method outperforms state-of-the-art baselines on standard MARL benchmarks, including a variety of SMAC II maps.

Autonomous exploration of cluttered environments requires efficient exploration strategies that guarantee safety against potential collisions with unknown random obstacles. This paper presents a novel approach combining a graph neural network-based exploration greedy policy with a safety shield to ensure safe navigation goal selection. The network is trained using reinforcement learning and the proximal policy optimization algorithm to maximize exploration efficiency while reducing the safety shield interventions. However, if the policy selects an infeasible action, the safety shield intervenes to choose the best feasible alternative, ensuring system consistency. Moreover, this paper proposes a reward function that includes a potential field based on the agent's proximity to unexplored regions and the expected information gain from reaching them. Overall, the approach investigated in this paper merges the benefits of the adaptability of reinforcement learning-driven exploration policies and the guarantee ensured by explicit safety mechanisms. Extensive evaluations in simulated environments demonstrate that the approach enables efficient and safe exploration in cluttered environments.

The sim-to-real gap remains a critical challenge in robotics, hindering the deployment of algorithms trained in simulation to real-world systems. We propose a flexible Real-to-Sim-to-Real (RSR) framework whose central contribution is an information-theoretic cost function that explicitly accounts for sim-to-real discrepancies. This cost balances two objectives, completing the task and steering the policy to collect real-world samples that are maximally informative for improving transfer. It can be integrated seamlessly into existing reinforcement learning algorithms (e.g., PPO, SAC) and ensures a balanced exploration of critical regions in the real domain. The framework treats differentiable simulation as optional: when a differentiable simulator is available, the collected informative data can also be used to tune simulator parameters. We implement the framework with the MuJoCo MJX platform and demonstrate its generality by evaluating on both manipulation tasks with a 6-DOF robotic arm and locomotion tasks on a legged robot. Empirical results show that our RSR loop yields more efficient data acquisition and substantially improves task performance in real-world that achieves a smoother sim-to-real transfer.

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

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

Amortized inference is the task of training a parametric model, such as a neural network, to approximate a distribution with a given unnormalized density where exact sampling is intractable. When sampling is implemented as a sequential decision-making process, reinforcement learning (RL) methods, such as generative flow networks, can be used to train the sampling policy. Off-policy RL training facilitates the discovery of diverse, high-reward candidates, but existing methods still face challenges in efficient exploration. We propose to use an adaptive training distribution (the \teacher) to guide the training of the primary amortized sampler (the \student). The \teacher, an auxiliary behavior model, is trained to sample high-loss regions of the \student and can generalize across unexplored modes, thereby enhancing mode coverage by providing an efficient training curriculum. We validate the effectiveness of this approach in a synthetic environment designed to present an exploration challenge, two diffusion-based sampling tasks, and four biochemical discovery tasks demonstrating its ability to improve sample efficiency and mode coverage. Source code is available at https://github.com/alstn12088/adaptive-teacher.

We pose uncertainty quantification and exploration in online decision-making as a problem of training and generation from an autoregressive sequence model, an area experiencing rapid innovation. Our approach rests on viewing uncertainty as arising from missing future outcomes that could be revealed through action choices, rather than from unobservable latent parameters of the environment. This reformulation aligns naturally with modern machine learning capabilities: we can i) train generative models through next-outcome prediction rather than fit explicit priors, ii) assess uncertainty through autoregressive generation rather than sampling latent parameters from posteriors, and iii) adapt to new information by extending the sequence model's context rather than explicit posterior updating. Our main theoretical result establishes a reduction from online decision-making to offline next-outcome prediction: Bayesian regret is controlled directly by the sequence model's offline prediction loss, without requiring an explicit latent-variable posterior. Experiments, including a semi-synthetic news recommendation task, show that autoregressive generation produces calibrated epistemic uncertainty and enables effective exploration by using article text as prior information to focus exploration on resolving remaining uncertainties.