# A Finite-Time Analysis of Multi-armed Bandits Problems with Kullback-Leibler Divergences

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Odalric-Ambrym Maillard,
Rémi Munos,
Gilles Stoltz
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Proceedings of the 24th Annual Conference on Learning Theory, PMLR 19:497-514, 2011.

#### Abstract

We consider a Kullback-Leibler-based algorithm for the stochastic multi-armed bandit problem in the case of distributions with finite supports(not necessarily known beforehand), whose asymptotic regret matches the lower bound of \citetBurnetas96. Our contribution is to provide a finite-time analysis of this algorithm;we get bounds whose main terms are smaller than the ones of previously known algorithms with finite-time analyses (like UCB-type algorithms).

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