A Finite-Time Analysis of Multi-armed Bandits Problems with   Kullback-Leibler Divergences
  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 (INRIA Lille - Nord Europe), R\'emi Munos   (INRIA Lille - Nord Europe), Gilles Stoltz (DMA, GREGH, ...
math.ST stat.TH