Maximum Entropy RL

Online Multi-Agent Reinforcement Learning (MARL) is a prominent framework for efficient agent coordination. Crucially, enhancing policy expressiveness is pivotal for achieving superior performance. Diffusion-based generative models are well-positioned to meet this demand, having demonstrated remarkable expressiveness and multimodal representation in image generation and offline settings. Yet, their potential in online MARL remains largely under-explored. A major obstacle is that the intractable likelihoods of diffusion models impede entropy-based exploration and coordination. To tackle this challenge, we propose among the first Online off-policy MARL framework using Diffusion policies (OMAD) to orchestrate coordination. Our key innovation is a relaxed policy objective that maximizes scaled joint entropy, facilitating effective exploration without relying on tractable likelihood. Complementing this, within the centralized training with decentralized execution (CTDE) paradigm, we employ a joint distributional value function to optimize decentralized diffusion policies. It leverages tractable entropy-augmented targets to guide the simultaneous updates of diffusion policies, thereby ensuring stable coordination. Extensive evaluations on MPE and MAMuJoCo establish our method as the new state-of-the-art across $10$ diverse tasks, demonstrating a remarkable $2.5\times$ to $5\times$ improvement in sample efficiency.

Stochastic Optimal Control provides a unified mathematical framework for solving complex decision-making problems, encompassing paradigms such as maximum entropy reinforcement learning(RL) and imitation learning(IL). However, conventional parametric policies often struggle to represent the multi-modality of the solutions. Though diffusion-based policies are aimed at recovering the multi-modality, they lack an explicit probability density, which complicates policy-gradient optimization. To bridge this gap, we propose MePoly, a novel policy parameterization based on polynomial energy-based models. MePoly provides an explicit, tractable probability density, enabling exact entropy maximization. Theoretically, we ground our method in the classical moment problem, leveraging the universal approximation capabilities for arbitrary distributions. Empirically, we demonstrate that MePoly effectively captures complex non-convex manifolds and outperforms baselines in performance across diverse benchmarks.

Real-world reinforcement learning often faces environment drift, but most existing methods rely on static entropy coefficients/target entropy, causing over-exploration during stable periods and under-exploration after drift, and leaving unanswered the principled question of how exploration intensity should scale with drift magnitude. We show that, under standard assumptions, entropy scheduling in non-stationary maximum-entropy RL can be cast as the dynamic-regret trade-off between tracking a drifting comparator and stabilizing updates, yielding a square-root scaling rule for the entropy weight in terms of a online non-stationarity proxy. Building on this, we propose AES--Adaptive Entropy Scheduling--which adaptively adjusts the entropy coefficient/temperature online using observable drift proxies during training, requiring almost no structural changes and incurring minimal overhead. Across 4 algorithm variants, 12 tasks, and 4 drift modes, AES significantly reduces the fraction of performance degradation caused by drift and accelerates recovery after abrupt changes.

Fitted $Q$-iteration (FQI) is a standard regression-based method for optimal control in offline reinforcement learning, but its stability under function approximation often relies on Bellman completeness, which requires Bellman images of the fitted class to remain in the class. We study Kullback--Leibler (KL)-regularized, or soft, FQI relative to a fixed reference policy without this assumption. Our key insight is that soft control locally inherits the contraction of policy evaluation in a discounted-occupancy norm. At the soft-optimal fixed point, the linearization of the soft Bellman operator is exactly the Bellman operator for the soft-optimal policy, which contracts in its discounted-occupancy norm; projection in the same norm preserves this contraction. Standard soft FQI instead projects under the offline state-action distribution and need not preserve this property. Motivated by this observation, we propose occupancy-reweighted soft FQI, which retains standard Bellman targets and least-squares updates while reweighting regressions by discounted-occupancy ratios induced by the current soft policy. Under $Q$-function realizability and local regularity, we establish local contraction and finite-sample convergence with estimated ratios, without Bellman completeness. We then use temperature annealing to convert the local result into global convergence from arbitrary initialization: sufficiently high temperature provides a globally contractive starting regime, while gradual cooling connects successive local contraction regions to any prescribed positive target temperature. Under an action-gap margin condition, switching at a fixed positive temperature to hard FQI with refreshed occupancy weights also yields population and finite-sample convergence to the unregularized optimum.

Diffusion models provide an expressive framework for sampling from complex, unnormalized distributions. In this work, we extend Maximum Entropy Reinforcement Learning (ME-RL) to diffusion-based policies by introducing Diffusion-Augmented Markov Decision Processes (DA-MDPs). DA-MDPs interpret each reverse-diffusion transition as an individual reinforcement-learning decision, while only the final denoised action is executed in the environment. Our DA-MDPs follow from a principled derivation based on the variational-inference formulation of ME-RL. By augmenting policy and target trajectories with intermediate diffusion variables, we obtain a tractable reverse-KL upper bound via the data-processing inequality. This bound decomposes across denoising transitions, yielding diffusion-augmented variants of soft rewards, value functions, and local policy objectives. This provides a general framework for adapting ME-RL algorithms to diffusion policies while differentiating through only one diffusion transition at a time. We instantiate the framework with PPO, REPPO, and a maximum-entropy extension of WPO. Experiments demonstrate improved continuous-control performance, benefits from additional diffusion steps, and memory-efficient training. On the StackCube and PushT manipulation tasks, DA-MDP methods learn alternative successful strategies from the same initial state and achieve higher success rates and generally higher success-weighted mode entropy than the Gaussian ME-RL baseline. We also demonstrate successful training when using action chunking.

At the heart of reinforcement learning are actions -- decisions made in response to observations of the environment. Actions are equally fundamental in the modeling of stochastic processes, as they trigger discontinuous state transitions and enable the flow of information through large, complex systems. In this paper, we unify the perspectives of stochastic processes and reinforcement learning through action-driven processes, and illustrate their application to spiking neural networks. Leveraging ideas from control-as-inference, we show that minimizing the Kullback-Leibler divergence between a policy-driven true distribution and a reward-driven model distribution for a suitably defined action-driven process is equivalent to maximum entropy reinforcement learning.

Reinforcement learning (RL) is a key paradigm for post-training large language models (LLMs), but the widely used Group Relative Policy Optimization (GRPO) often suffers from entropy collapse: exploration quickly disappears, policies converge prematurely, and sample diversity declines, ultimately harming training effectiveness. Existing remedies, including entropy bonuses and clip-based methods, rarely keep entropy within a stable exploration regime and often introduce oscillatory entropy or reward degradation. In this work, we identify a previously overlooked asymmetry in entropy dynamics: under high-temperature sampling, positive and negative samples have opposite effects on policy entropy. Specifically, high-temperature positive samples promote entropy growth, whereas negative samples suppress it. We provide a qualitative theoretical explanation for this phenomenon: when entropy decreases during policy updates, its derivative with respect to temperature is strictly positive under positive sample updates, indicating that high-temperature positive samples can counteract entropy decay, thereby slowing entropy collapse and potentially reversing it. Motivated by this insight, we propose SCOPE-RL, a stable entropy control framework through a regularization term constructed from temperature-adaptive positive samples. Extensive experiments show that SCOPE-RL consistently outperforms strong RL baselines on both Pass@1 and Pass@k. Our results provide evidence that escaping entropy collapse can improve reasoning performance, while our quantitative empirical analysis further reveals a non-monotonic entropy-performance relationship, with an optimal level of exploration for RL post-training in reasoning LLMs. Our code is available at https://github.com/597358816/SCOPE-RL.

A major bottleneck in scientific discovery consists of narrowing an exponentially large set of objects, such as proteins or molecules, to a small set of promising candidates with desirable properties. While this process can rely on expert knowledge, recent methods leverage reinforcement learning (RL) guided by a proxy reward function to enable this filtering. By employing various forms of entropy regularization, these methods aim to learn samplers that generate diverse candidates that are highly rated by the proxy function. In this work, we make two main contributions. First, we show that these methods are liable to generate overly diverse, suboptimal candidates in large search spaces. To address this issue, we introduce a novel unified operator that combines several regularized RL operators into a general framework that better targets peakier sampling distributions. Secondly, we offer a novel, robust RL perspective of this filtering process. The regularization can be interpreted as robustness to a compositional form of uncertainty in the proxy function (i.e., the true evaluation of a candidate differs from the proxy's evaluation). Our analysis leads us to a novel, easy-to-use algorithm we name trajectory general mellowmax (TGM): we show it identifies higher quality, diverse candidates than baselines in both synthetic and real-world tasks. Code: https://github.com/marcojira/tgm.

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.