Improved Analysis of UCRL2 with Empirical Bernstein Inequality

Abstract

We consider the problem of exploration-exploitation in communicating Markov Decision Processes. We provide an analysis of UCRL2 with Empirical Bernstein inequalities (UCRL2B). For any MDP with $S$ states, $A$ actions, $\Gamma \le S$ next states and diameter $D$, the regret of UCRL2B is bounded as $\tilde{O}(\sqrt{D\Gamma SAT})$.

Document in support of the tutorial at ALT 2019