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