A General Framework for Sample-Efficient Function Approximation in Reinforcement Learning

Zixiang Chen, Chris Junchi Li, Huizhuo Yuan, Quanquan Gu, Michael Jordan

Keywords: general function approximation, sample-efficient RL, optimization-based exploration, Eluder dimension, Bellman rank, witness rank, complexity measure, hypothesis class

TL;DR: We provide a unified framework that nearly includes all model-free and model-based RL classes while maintaining sharp sample efficiency.

Abstract: With the increasing need for handling large state and action spaces, general function approximation has become a key technique in reinforcement learning (RL). In this paper, we propose a general framework that unifies model-based and model-free RL, and an Admissible Bellman Characterization (ABC) class that subsumes nearly all Markov decision process (MDP) models in the literature for tractable RL. We propose a novel estimation function with decomposable structural properties for optimization-based exploration and the functional Eluder dimension as a complexity measure of the ABC class. Under our framework, a new sample-efficient algorithm namely OPtimization-based ExploRation with Approximation (OPERA) is proposed, achieving regret bounds that match or improve over the best-known results for a variety of MDP models. In particular, for MDPs with low Witness rank, under a slightly stronger assumption, OPERA improves the state-of-the-art sample complexity results by a factor of $dH$. Our framework provides a generic interface to design and analyze new RL models and algorithms.

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