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Thompson Sampling is one of the most effective methods for contextual banditsand has been generalized to posterior sampling for certain MDP settings.However, existing posterior sampling methods for reinforcement learning arelimited by being model-based or lack worst-case theoretical guarantees beyondlinear MDPs. This paper proposes a new model-free formulation of posteriorsampling that applies to more general episodic reinforcement learning problemswith theoretical guarantees. We introduce novel proof techniques to show thatunder suitable conditions, the worst-case regret of our posterior samplingmethod matches the best known results of optimization based methods. In thelinear MDP setting with dimension, the regret of our algorithm scales linearlywith the dimension as compared to a quadratic dependence of the existingposterior sampling-based exploration algorithms.

A Provably Efficient Model-Free Posterior Sampling Method for Episodic Reinforcement Learning