Deviations of Stochastic Bandit Regret

摘要

This paper studies the deviations of the regret in a stochastic multi-armed bandit problem. When the total number of plays n is known beforehand by the agent, Audibert et al. (2009) exhibit a policy such that with probability at least 1 - 1, the regret of the policy is of order logn. They have also shown that such a property is not shared by the popular UCBl policy of Auer et al. (2002). This work first answers an open question: it extends this negative result to any anytime policy. The second contribution of this paper is to design anytime robust policies for specific multi-armed bandit problems in which some restrictions are put on the set of possible distributions of the different arms.