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 \cite{Burnetas96}. 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).
Odalric-Ambrym Maillard, Rémi Munos, Gilles Stoltz. A Finite-Time Analysis of Multi-armed Bandits Problems with Kullback-Leibler Divergences. 24th Annual Conference on Learning Theory : COLT'11, Jul 2011, Budapest, Hungary. pp.18. ⟨inria-00574987v2⟩
