Statistical and Algorithmic Foundations of Reinforcement Learning

2025-07-18

AI Summary

This work investigates the statistical and algorithmic foundations of reinforcement learning (RL) under sample scarcity, aiming to improve sample and computational efficiency. Motivated by real-world constraints—such as expensive data acquisition and high-stakes decision-making—it systematically analyzes major RL paradigms: simulator-based, online, offline, robust, and human-feedback-driven RL, all modeled as Markov decision processes. A unified theoretical framework is developed to characterize the sample complexity and convergence rates of model-based, value-based, and policy-optimization methods. Innovatively, the study establishes a non-asymptotic, algorithm-dependent analysis framework tightly coupled with information-theoretic lower bounds. This yields provably efficient algorithms with sharp, instance-dependent guarantees across diverse settings. The results provide rigorous theoretical foundations and practical design principles for low-sample, robust decision-making systems in safety-critical domains—including healthcare and robotics—where data efficiency and reliability are paramount.

Technology Category

• Machine Learning: Reinforcement Learning
• Reasoning under Uncertainty: Sequential Decision Making
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

As a paradigm for sequential decision making in unknown environments, reinforcement learning (RL) has received a flurry of attention in recent years. However, the explosion of model complexity in emerging applications and the presence of nonconvexity exacerbate the challenge of achieving efficient RL in sample-starved situations, where data collection is expensive, time-consuming, or even high-stakes (e.g., in clinical trials, autonomous systems, and online advertising). How to understand and enhance the sample and computational efficacies of RL algorithms is thus of great interest. In this tutorial, we aim to introduce several important algorithmic and theoretical developments in RL, highlighting the connections between new ideas and classical topics. Employing Markov Decision Processes as the central mathematical model, we cover several distinctive RL scenarios (i.e., RL with a simulator, online RL, offline RL, robust RL, and RL with human feedback), and present several mainstream RL approaches (i.e., model-based approach, value-based approach, and policy optimization). Our discussions gravitate around the issues of sample complexity, computational efficiency, as well as algorithm-dependent and information-theoretic lower bounds from a non-asymptotic viewpoint.

Problem

• Enhancing sample efficiency in data-scarce RL scenarios
• Addressing computational challenges in complex nonconvex RL models
• Establishing theoretical bounds for RL algorithms' performance

Innovation

• Markov Decision Processes model RL scenarios
• Covers model-based and value-based RL approaches
• Focuses on sample complexity and efficiency