Optimal Posterior Sampling for Policy Identification in Tabular Markov Decision Processes

Problem
This paper addresses the $(\varepsilon, \delta)$-PAC policy identification problem in finite-horizon episodic Markov Decision Processes (MDPs). Existing methods provide finite-time guarantees for approximate settings ($\varepsilon > 0$) but are hindered by high computational costs and suboptimal dependence on $\log(1/\delta)$. The authors propose a new approach that aims to improve both computational efficiency and theoretical guarantees, filling a gap in the literature regarding scalable and effective policy identification in tabular MDPs. This work is presented as a preprint and has not yet undergone peer review.

Method
The authors introduce a randomized algorithm that integrates posterior sampling with an online learning framework to enhance exploration in MDPs. The proposed method achieves asymptotic optimality in sample complexity and aligns with the posterior contraction rate. The algorithm operates with a computational complexity of $O(S^2AH)$ per episode, where $S$ is the state space size, $A$ is the action space size, and $H$ is the horizon length. This efficiency matches that of standard model-based approaches while avoiding the suboptimal polynomial dependence on $\log(1/\delta)$ that characterizes previous algorithms like MOCA and PEDEL. The method’s design emphasizes both theoretical robustness and practical applicability in policy identification tasks.

Results
The authors demonstrate that their algorithm achieves significant improvements over existing baselines in terms of sample complexity and computational efficiency. While specific numerical results are not detailed in the abstract, the paper claims that their method maintains meaningful guarantees in the asymptotic regime, which is a notable advancement over prior work. The theoretical framework provided supports the algorithm’s performance, suggesting that it can effectively identify optimal policies with fewer samples compared to traditional methods.

Limitations
The authors acknowledge that their approach, while efficient, is still constrained to tabular MDPs, which may limit its applicability to more complex, continuous, or high-dimensional state-action spaces. Additionally, the reliance on posterior sampling may introduce variability in performance depending on the quality of the prior distributions used. The paper does not address potential scalability issues when extending the method to larger or more complex MDPs, nor does it explore the impact of different exploration strategies on the overall performance.

Why it matters
This work has significant implications for the field of reinforcement learning, particularly in the context of policy identification in MDPs. By providing a computationally efficient and theoretically sound method, the authors contribute to the development of scalable algorithms that can be applied in real-world scenarios where decision-making under uncertainty is critical. The insights gained from this research could inform future studies on policy optimization and exploration strategies, potentially leading to advancements in both theoretical understanding and practical implementations in various applications, including robotics, finance, and healthcare.

Authors: Cyrille Kone, Kevin Jamieson
Source: arXiv:2605.03921
URL: https://arxiv.org/abs/2605.03921v1