Deviations of Stochastic Bandit Regret

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/n, the regret of the policy is of order log n. They have also shown that such a property is not shared by the popular ucb1 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.

• Type: Journal
• Year: 2011
• Where: ALT
• Authors: Antoine Salomon, Jean-Yves Audibert
• Keywords: ALT 2011, Bandit Problems, Erent, Machine Learning, Open Question