Partial Differential Equations (PDEs) describe phenomena ranging from turbulence and epidemics to quantum mechanics and financial markets. Despite recent advances in computational science, solving such PDEs for real-world applications remains prohibitively expensive because of the necessity of resolving a broad range of spatiotemporal scales. In turn, practitioners often rely on coarse-grained approximations of the original PDEs, trading off accuracy for reduced computational resources. To mitigate the loss of detail inherent in such approximations, closure models are employed to represent unresolved spatiotemporal interactions. We present a framework for developing closure models for PDEs using synthetic data acquired through the method of manufactured solutions. These data are used in conjunction with reinforcement learning to provide closures for coarse-grained PDEs. We illustrate the efficacy of our method using the one-dimensional and two-dimensional Burgers' equations and the two-dimensional advection equation. Moreover, we demonstrate that closure models trained for inhomogeneous PDEs can be effectively generalized to homogeneous PDEs. The results demonstrate the potential for developing accurate and computationally efficient closure models for systems with scarce data.

The fine-tuning of pre-trained large language models (LLMs) using reinforcement learning (RL) is generally formulated as direct policy optimization. This approach was naturally favored as it efficiently improves a pretrained LLM, seen as an initial policy. Another RL paradigm, Q-learning methods, has received far less attention in the LLM community while demonstrating major success in various non-LLM RL tasks. In particular, Q-learning effectiveness comes from its sample efficiency and ability to learn offline, which is particularly valuable given the high computational cost of sampling with LLMs. However, naively applying a Q-learning-style update to the model's logits is ineffective due to the specificity of LLMs. Our core contribution is to derive theoretically grounded loss functions from Bellman equations to adapt Q-learning methods to LLMs. To do so, we carefully adapt insights from the RL literature to account for LLM-specific characteristics, ensuring that the logits become reliable Q-value estimates. We then use this loss to build a practical algorithm, ShiQ for Shifted-Q, that supports off-policy, token-wise learning while remaining simple to implement. Finally, we evaluate ShiQ on both synthetic data and real-world benchmarks, e.g., UltraFeedback and BFCL-V3, demonstrating its effectiveness in both single-turn and multi-turn LLM settings

Sparse and delayed reward functions pose a significant obstacle for real-world Reinforcement Learning (RL) applications. In this work, we propose Attention-based REward Shaping (ARES), a general and robust algorithm which uses a transformer's attention mechanism to generate shaped rewards and create a dense reward function for any environment. ARES requires a set of episodes and their final returns as input. It can be trained entirely offline and is able to generate meaningful shaped rewards even when using small datasets or episodes produced by agents taking random actions. ARES is compatible with any RL algorithm and can handle any level of reward sparsity. In our experiments, we focus on the most challenging case where rewards are fully delayed until the end of each episode. We evaluate ARES across a diverse range of environments, widely used RL algorithms, and baseline methods to assess the effectiveness of the shaped rewards it produces. Our results show that ARES can significantly improve learning in delayed reward settings, enabling RL agents to train in scenarios that would otherwise require impractical amounts of data or even be unlearnable. To our knowledge, ARES is the first approach that works fully offline, remains robust to extreme reward delays and low-quality data, and is not limited to goal-based tasks.

Claire chatted to Lerrel Pinto from New York University about using machine learning to train robots to adapt to new environments. Lerrel Pinto is an Assistant Professor of Computer Science at New York University (NYU). His research is aimed at getting robots to generalize and adapt in the messy world we live in. His lab focuses broadly on robot learning and decision making, with an emphasis on large-scale learning (both data and models); representation learning for sensory data; developing algorithms to model actions and behaviour; reinforcement learning for adapting to new scenarios; and building open-source, affordable robots.

A central challenge in reinforcement learning (RL) is its dependence on extensive real-world interaction data to learn task-specific policies. While recent work demonstrates that large language models (LLMs) can mitigate this limitation by generating synthetic experience (noted as imaginary rollouts) for mastering novel tasks, progress in this emerging field is hindered due to the lack of a standard benchmark. To bridge this gap, we introduce ImagineBench, the first comprehensive benchmark for evaluating offline RL algorithms that leverage both real rollouts and LLM-imaginary rollouts. The key features of ImagineBench include: (1) datasets comprising environment-collected and LLM-imaginary rollouts; (2) diverse domains of environments covering locomotion, robotic manipulation, and navigation tasks; and (3) natural language task instructions with varying complexity levels to facilitate language-conditioned policy learning. Through systematic evaluation of state-of-the-art offline RL algorithms, we observe that simply applying existing offline RL algorithms leads to suboptimal performance on unseen tasks, achieving 35.44% success rate in hard tasks in contrast to 64.37% of method training on real rollouts for hard tasks. This result highlights the need for algorithm advancements to better leverage LLM-imaginary rollouts. Additionally, we identify key opportunities for future research: including better utilization of imaginary rollouts, fast online adaptation and continual learning, and extension to multi-modal tasks. Our code is publicly available at https://github.com/LAMDA-RL/ImagineBench.

Federated reinforcement learning (FRL) methods usually share the encrypted local state or policy information and help each client to learn from others while preserving everyone's privacy. In this work, we propose that sharing the approximated behavior metric-based state projection function is a promising way to enhance the performance of FRL and concurrently provides an effective protection of sensitive information. We introduce FedRAG, a FRL framework to learn a computationally practical projection function of states for each client and aggregating the parameters of projection functions at a central server. The FedRAG approach shares no sensitive task-specific information, yet provides information gain for each client. We conduct extensive experiments on the DeepMind Control Suite to demonstrate insightful results.

A Markov Decision Process (MDP) is conceived, where the time horizon includes multiple charging and operating periods in a day, while each period is further divided into multiple time steps. To overcome the challenge of long-range multi-phase planning with sparse reward, we conceive Hierarchical DRL (HDRL) for decoupling the original MDP into a high-level Semi-MDP (SMDP) and multiple low-level MDPs. The Hierarchical Double Deep Q-Network (HDDQN)-Hindsight Experience Replay (HER) algorithm is proposed for simultaneously solving the decision problems arising at different temporal resolutions. As a result, the high-level agent learns an effective policy for prescribing the charging targets for every charging period, while the low-level agent learns an optimal policy for setting the charging power of every time step within a single charging period, with the aim of minimizing the charging costs while meeting the charging target. It is proved that the flat policy constructed by superimposing the optimal high-level policy and the optimal low-level policy performs as well as the optimal policy of the original MDP . Since jointly learning both levels of policies is challenging due to the non-stationarity of the high-level agent and the sampling inefficiency of the low-level agent, we divide the joint learning process into two phases and exploit our new HER algorithm to manipulate the experience replay buffers for both levels of agents. Numerical experiments are performed with the aid of real-world data to evaluate the performance of the proposed algorithm. Index T erms Deep Reinforcement Learning; Electric Bus; Hierarchical Reinforcement learning; Charging Control A CRONYMS DDQN Double Deep Q Network DNN Deep Neural Network DQL Double Q-learning DQN Deep Q Network DRL Deep Reinforcement Learning EB Electric Bus EBCSP Electric Bus Charging Scheduling Problem GA Genetic Algorithm GHG GreenHouse Gas HAC Hierarchical Actor-Critic HDDQN Hierarchical Double Deep Q Network HDRL Hierarchical Deep Reinforcement Learning HER Hindsight Experience Replay HRL Hierarchical Reinforcement Learning IA Immune Algorithm MDP Markov Decision Process MILP Mixed Integer Linear Programming ML Machine Learning MRP Markov Reward Process RES Renewable Energy Source RL Reinforcement Learning RO Robust Optimization RTEM Real Time Energy Market 1 J. Qi and L. Lei are with the School of Engineering, University of Guelph, Guelph, ON N1G 2W1, Canada, jiaju@uoguelph.ca;

The rapid advancements in quantum computing (QC) and machine learning (ML) have led to the emergence of quantum machine learning (QML), which integrates the strengths of both fields. Among QML approaches, variational quantum circuits (VQCs), also known as quantum neural networks (QNNs), have shown promise both empirically and theoretically. However, their broader adoption is hindered by reliance on quantum hardware during inference. Hardware imperfections and limited access to quantum devices pose practical challenges. To address this, the Quantum-Train (QT) framework leverages the exponential scaling of quantum amplitudes to generate classical neural network parameters, enabling inference without quantum hardware and achieving significant parameter compression. Yet, designing effective quantum circuit architectures for such quantum-enhanced neural programmers remains non-trivial and often requires expertise in quantum information science. In this paper, we propose an automated solution using differentiable optimization. Our method jointly optimizes both conventional circuit parameters and architectural parameters in an end-to-end manner via automatic differentiation. We evaluate the proposed framework on classification, time-series prediction, and reinforcement learning tasks. Simulation results show that our method matches or outperforms manually designed QNN architectures. This work offers a scalable and automated pathway for designing QNNs that can generate classical neural network parameters across diverse applications.

We propose a new framework for multi-agent reinforcement learning (MARL), where the agents cooperate in a time-evolving network with latent community structures and mixed memberships. Unlike traditional neighbor-based or fixed interaction graphs, our community-based framework captures flexible and abstract coordination patterns by allowing each agent to belong to multiple overlapping communities. Each community maintains shared policy and value functions, which are aggregated by individual agents according to personalized membership weights. We also design actor-critic algorithms that exploit this structure: agents inherit community-level estimates for policy updates and value learning, enabling structured information sharing without requiring access to other agents' policies. Importantly, our approach supports both transfer learning by adapting to new agents or tasks via membership estimation, and active learning by prioritizing uncertain communities during exploration. Theoretically, we establish convergence guarantees under linear function approximation for both actor and critic updates. To our knowledge, this is the first MARL framework that integrates community structure, transferability, and active learning with provable guarantees.

Motivated by practical applications where stable long-term performance is critical-such as robotics, operations research, and healthcare-we study the problem of distributionally robust (DR) average-reward reinforcement learning. We propose two algorithms that achieve near-optimal sample complexity. The first reduces the problem to a DR discounted Markov decision process (MDP), while the second, Anchored DR Average-Reward MDP, introduces an anchoring state to stabilize the controlled transition kernels within the uncertainty set. Assuming the nominal MDP is uniformly ergodic, we prove that both algorithms attain a sample complexity of $\widetilde{O}\left(|\mathbf{S}||\mathbf{A}| t_{\mathrm{mix}}^2\varepsilon^{-2}\right)$ for estimating the optimal policy as well as the robust average reward under KL and $f_k$-divergence-based uncertainty sets, provided the uncertainty radius is sufficiently small. Here, $\varepsilon$ is the target accuracy, $|\mathbf{S}|$ and $|\mathbf{A}|$ denote the sizes of the state and action spaces, and $t_{\mathrm{mix}}$ is the mixing time of the nominal MDP. This represents the first finite-sample convergence guarantee for DR average-reward reinforcement learning. We further validate the convergence rates of our algorithms through numerical experiments.