Learning Adversarial Markov Decision Processes with Bandit Feedback and Unknown Transition

We consider the task of learning in episodic finitehorizon Markov decision processes with an unknown transition function, bandit feedback, and adversarial losses. We propose an efficient algorithm that achieves O(LjXj p jAjT) regret with high probability, where L is the horizon, jXj the number of states, jAj the number of actions, and T the number of episodes. To our knowledge, our algorithm is the first to ensure O( p T) regret in this challenging setting; in fact it achieves the same regret as (Rosenberg and Mansour, 2019a) who consider the easier setting with full-information. Our key contributions are two-fold: A tighter confidence set for the transition function; and an optimistic loss estimator that is inversely weighted by an upper occupancy bound.