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

Odalric-Ambrym Maillard (1) , Rémi Munos (1) , Gilles Stoltz (2, 3)

1 SEQUEL - Sequential Learning
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC

We consider a Kullback-Leibler-based algorithm for the stochastic multi-armed bandit prob- lem in the case of distributions with nite support, whose asymptotic regret matches the lower bound of Burnetas and Katehakis (1996). Our contribution is to provide a nite-time analysis of this algorithm.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Apprentissage [cs.LG]

Odalric-Ambrym Maillard, Rémi Munos, Gilles Stoltz. A Finite-Time Analysis of Multi-armed Bandits Problems with Kullback-Leibler Divergences. [Technical Report] 2011, pp.18. ⟨inria-00574987v1⟩