Episodic Reinforcement Learning in Finite MDPs: Minimax Lower Bounds Revisited

In this paper, we propose new problem-independent lower bounds on the sample complexity and regret in episodic MDPs, with a particular focus on the non-stationary case in which the transition kernel is allowed to change in each stage of the episode. Our main contribution is a lower bound of Omega((H(3)SA/epsilon(2)) log(1/delta)) on the sample complexity of an (epsilon, delta)-PAC algorithm for best policy identification in a non-stationary MDP, relying on a construction of "hard MDPs" which is different from the ones previously used in the literature. Using this same class of MDPs, we also provide a rigorous proof of the Omega(root H(3)SAT) regret bound for non-stationary MDPs. Finally, we discuss connections to PAC-MDP lower bounds.