Section: New Results

Deviations of Stochastic Bandit Regret

Participant : Jean-Yves Audibert.

Collaboration with: Antoine Salomon (École des Ponts)

The work [19] 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, previous works exhibit a policy such that with probability at least $1-1/n$, the regret of the policy is of order $logn$. They have also shown that such a property is not shared by the popular ucb1 policy. 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.