Decision making in these systems has a long history, yet, if the state is not fully observed acting optimally in such systems is notoriously hard.

We study off-policy reinforcement learning for controlling continuous-time Markov diffusion processes with discrete-time observations and actions. We consider model-free algorithms with function approximation that learn value and advantage functions directly from data, without unrealistic structural assumptions on the dynamics. Leveraging the ellipticity of the diffusions, we establish a new class of Hilbert-space positive definiteness and boundedness properties for the Bellman operators. Based on these properties, we propose the Sobolev-prox fitted $q$-learning algorithm, which learns value and advantage functions by iteratively solving least-squares regression problems. We derive oracle inequalities for the estimation error, governed by (i) the best approximation error of the function classes, (ii) their localized complexity, (iii) exponentially decaying optimization error, and (iv) numerical discretization error. These results identify ellipticity as a key structural property that renders reinforcement learning with function approximation for Markov diffusions no harder than supervised learning.

The predominant approach in reinforcement learning is to assign credit to actions based on the expected return. However, we show that the return may depend on the policy in a way which could lead to excessive variance in value estimation and slow down learning. Instead, we show that the advantage function can be interpreted as causal effects and shares similar properties with causal representations. Based on this insight, we propose Direct Advantage Estimation (DAE), a novel method that can model the advantage function and estimate it directly from on-policy data while simultaneously minimizing the variance of the return without requiring the (action-)value function. We also relate our method to Temporal Difference methods by showing how value functions can be seamlessly integrated into DAE. The proposed method is easy to implement and can be readily adapted by modern actor-critic methods. We evaluate DAE empirically on three discrete control domains and show that it can outperform generalized advantage estimation (GAE), a strong baseline for advantage estimation, on a majority of the environments when applied to policy optimization.

Cross-Domain Offline Reinforcement Learning aims to train an agent deployed in the target environment, leveraging both a limited target domain dataset and a source domain dataset with (possibly) sufficient data coverage. Due to the underlying dynamics misalignment between the source and target domain, simply merging the data from two datasets may incur inferior performance. Recent advances address this issue by selectively sharing source domain samples that exhibit dynamics alignment with the target domain. However, these approaches focus solely on dynamics alignment and overlook \textit{value alignment}, i.e., selecting high-quality, high-value samples from the source domain. In this paper, we first demonstrate that both dynamics alignment and value alignment are essential for policy learning, by examining the limitations of the current theoretical framework for cross-domain RL and establishing a concrete sub-optimality gap of a policy trained on the source domain and evaluated on the target domain. Motivated by the theoretical insights, we propose to selectively share those source domain samples with both high dynamics and value alignment and present our \textbf{\underline{D}}ynamics- and \textbf{\underline{V}}alue-aligned \textbf{\underline{D}}ata \textbf{\underline{F}}iltering (DVDF) method. We design a range of dynamics shift settings, including kinematic and morphology shifts, and evaluate DVDF on various tasks and datasets, as well as in challenging extremely low-data settings where the target domain dataset contains only 5,000 transitions. Extensive experiments demonstrate that DVDF consistently outperforms prior strong baselines and delivers exceptional performance across multiple tasks and datasets.

We present BLINQ, a new model-based algorithm that learns the Whittle indices of an indexable, communicating and unichain Markov Decision Process (MDP). Our approach relies on building an empirical estimate of the MDP and then computing its Whittle indices using an extended version of a state-of-the-art existing algorithm. We provide a proof of convergence to the Whittle indices we want to learn as well as a bound on the time needed to learn them with arbitrary precision. Moreover, we investigate its computational complexity. Our numerical experiments suggest that BLINQ significantly outperforms existing Q-learning approaches in terms of the number of samples needed to get an accurate approximation. In addition, it has a total computational cost even lower than Q-learning for any reasonably high number of samples. These observations persist even when the Q-learning algorithms are speeded up using pre-trained neural networks to predict Q-values.

In cooperative Multi-Agent Reinforcement Learning (MARL), efficient exploration is crucial for optimizing the performance of joint policy. However, existing methods often update joint policies via independent agent exploration, without coordination among agents, which inherently constrains the expressive capacity and exploration of joint policies. To address this issue, we propose a conductor-based joint policy framework that directly enhances the expressive capacity of joint policies and coordinates exploration. In addition, we develop a Hierarchical Conductor-based Policy Optimization (HCPO) algorithm that instructs policy updates for the conductor and agents in a direction aligned with performance improvement. A rigorous theoretical guarantee further establishes the monotonicity of the joint policy optimization process. By deploying local conductors, HCPO retains centralized training benefits while eliminating inter-agent communication during execution. Finally, we evaluate HCPO on three challenging benchmarks: Star-CraftII Multi-agent Challenge, Multi-agent MuJoCo, and Multi-agent Particle Environment. The results indicate that HCPO outperforms competitive MARL baselines regarding cooperative efficiency and stability.