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

With the increasing need for handling large state and action spaces, general function approximation has become a key technique in reinforcement learning problems. In this paper, we propose a unified framework that integrates both model-based and model-free reinforcement learning and subsumes nearly all Markov decision process (MDP) models in the existing literature for tractable RL. We propose a novel estimation function with decomposable structural properties for optimization-based exploration and use the functional Eluder dimension with respect to an admissible Bellman characterization function as a complexity measure of the model 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 study and design new RL models and algorithms.