Statistical Foundations of Reinforcement Learning: A Non-Asymptotic Perspective

Abstract

Reinforcement learning (RL) embodies a foundational paradigm for sequential decision-making in the face of uncertainty. The rapid growth of model complexity in emerging applications has significantly amplified the challenges of achieving data-efficient RL, particularly in sample-starved scenarios where data collection may be costly, time-consuming, or even high-stakes. Consequently, understanding and improving the data efficiency of RL algorithms has become a central problem of both fundamental theoretical interest and practical importance. Despite decades of research, the statistical underpinnings of RL remained remarkably underdeveloped until relatively recently, particularly in the finite-sample regimes most relevant to modern practice. Over the past few years, there has been a surge of activity advancing the frontiers of non-asymptotic statistical RL theory, drawing on ideas from high-dimensional statistics and probability, information theory, and statistical learning theory. In this monograph, we present a non-asymptotic treatment for RL based on tabular Markov decision processes, focusing on three canonical sampling mechanisms --- RL with a generative model, online RL, and offline RL --- together with two algorithmic paradigms: model-based and model-free approaches. Centered around non-asymptotic sample complexity analysis, our treatment emphasizes minimax-optimal algorithm design, particularly methods that attain statistical optimality without significant burn-in costs, as well as sharp statistical characterizations of several widely used RL algorithms. Whenever possible, we provide largely self-contained analyses together with intuitive explanations. We also briefly discuss several extensions, such as robust RL, competitive multi-agent RL, federated RL, uncertainty quantification, and RL from human feedback.