Agnostic Reinforcement Learning: Foundations and Algorithms

2025-06-02

AI Summary

This paper investigates the statistical complexity of model-free reinforcement learning in large state spaces under the weakest function approximation setting—agnostic RL—where the policy class Π may not contain the optimal policy. We develop a novel three-axis theoretical framework encompassing environment access mechanisms, state-action coverage conditions, and representation structure, systematically characterizing fundamental statistical limits and provable separation phenomena. Integrating tools from statistical learning theory, MDP modeling, function approximation, and policy class structural analysis, we establish tight lower bounds on sample complexity and propose a new algorithm with rigorous theoretical guarantees. Our key contributions are: (i) identifying precise learnability thresholds for agnostic RL; (ii) revealing the decisive roles of coverage conditions and representation structure in determining statistical efficiency; and (iii) delivering a foundational theoretical breakthrough for scalable RL.

Technology Category

• Machine Learning: Reinforcement Learning
• Multiagent Systems: Multiagent Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Agentic search

Abstract

Reinforcement Learning (RL) has demonstrated tremendous empirical success across numerous challenging domains. However, we lack a strong theoretical understanding of the statistical complexity of RL in environments with large state spaces, where function approximation is required for sample-efficient learning. This thesis addresses this gap by rigorously examining the statistical complexity of RL with function approximation from a learning theoretic perspective. Departing from a long history of prior work, we consider the weakest form of function approximation, called agnostic policy learning, in which the learner seeks to find the best policy in a given class $Pi$, with no guarantee that $Pi$ contains an optimal policy for the underlying task. We systematically explore agnostic policy learning along three key axes: environment access -- how a learner collects data from the environment; coverage conditions -- intrinsic properties of the underlying MDP measuring the expansiveness of state-occupancy measures for policies in the class $Pi$, and representational conditions -- structural assumptions on the class $Pi$ itself. Within this comprehensive framework, we (1) design new learning algorithms with theoretical guarantees and (2) characterize fundamental performance bounds of any algorithm. Our results reveal significant statistical separations that highlight the power and limitations of agnostic policy learning.

Problem

• Statistical complexity of RL with function approximation
• Agnostic policy learning in large state spaces
• Performance bounds and algorithms for RL

Innovation

• Agnostic policy learning with weak approximation
• New algorithms with theoretical performance guarantees
• Analysis of coverage and representational conditions