A Provably Efficient Model-Free Posterior Sampling Method for Episodic Reinforcement Learning
This addresses the problem of efficient exploration in reinforcement learning for researchers and practitioners, offering a provably efficient model-free alternative to existing methods.
The paper tackles the limitation of existing posterior sampling methods in reinforcement learning by proposing a model-free formulation with theoretical guarantees for episodic RL problems, achieving worst-case regret that matches optimization-based methods and showing linear dimension scaling in linear MDPs compared to quadratic dependence in prior work.
Thompson Sampling is one of the most effective methods for contextual bandits and has been generalized to posterior sampling for certain MDP settings. However, existing posterior sampling methods for reinforcement learning are limited by being model-based or lack worst-case theoretical guarantees beyond linear MDPs. This paper proposes a new model-free formulation of posterior sampling that applies to more general episodic reinforcement learning problems with theoretical guarantees. We introduce novel proof techniques to show that under suitable conditions, the worst-case regret of our posterior sampling method matches the best known results of optimization based methods. In the linear MDP setting with dimension, the regret of our algorithm scales linearly with the dimension as compared to a quadratic dependence of the existing posterior sampling-based exploration algorithms.