Improved Analysis of UCRL2 with Empirical Bernstein Inequality

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, $\Gamma \leq S$ next states and diameter $D$, the regret of UCRL2B is bounded as $\widetilde{O}(\sqrt{D\Gamma S A T})$.