Distributional reinforcement learning improves performance by capturing environmental stochasticity, but a comprehensive theoretical understanding of its effectiveness remains elusive. In addition, the intractable element of the infinite dimensionality of distributions has been overlooked. In this paper, we present a regret analysis of distributional reinforcement learning with general value function approximation in a finite episodic Markov decision process setting. We first introduce a key notion of Bellman unbiasedness which is essential for exactly learnable and provably efficient distributional updates in an online manner. Among all types of statistical functionals for representing infinite-dimensional return distributions, our theoretical results demonstrate that only moment functionals can exactly capture the statistical information. Secondly, we propose a provably efficient algorithm, SF-LSVI, that achieves a tight regret bound of $\tilde{O}(d_E H^{\frac{3}{2}}\sqrt{K})$ where $H$ is the horizon, $K$ is the number of episodes, and $d_E$ is the eluder dimension of a function class.

To design reward that align with human goals, Reinforcement Learning from Human Feedback (RLHF) has emerged as a prominent technique for learning reward functions from human preferences and optimizing models using reinforcement learning algorithms. However, existing RLHF methods often misinterpret trajectories as being generated by an optimal policy, causing inaccurate likelihood estimation and suboptimal learning. To address this, we propose Policy-labeled Preference Learning (PPL) within the Direct Preference Optimization (DPO) framework, which resolves these likelihood mismatch problems by modeling human preferences with regret, reflecting the efficiency of executed policies. Additionally, we introduce a contrastive KL regularization term derived from regret-based principles to enhance sequential contrastive learning. Experiments in high-dimensional continuous control environments demonstrate PPL's significant improvements in offline RLHF performance and its effectiveness in online settings.

This paper addresses the problem of multi-risk measure agnostic multi-armed bandits in heavy-tailed reward settings. We propose a framework that leverages novel deviation inequalities for the $1$-Wasserstein distance to construct confidence intervals for Lipschitz risk measures. The distributional LCB (DistLCB) algorithm is introduced, which achieves asymptotic optimality by deriving the first lower bounds for risk measure aware bandits with explicit sub-optimality gap dependencies. The DistLCB is further extended to multi-risk objectives, which enables Pareto-optimal solutions that consider multiple aspects of reward distributions. Additionally, we provide a regret analysis that includes both gap-dependent and gap-independent bounds for multi-risk settings. Experiments validate the effectiveness of the proposed methods in synthetic and real-world applications.