Robustness of Anytime Bandit Policies

Antoine Salomon (1) , Jean-Yves Audibert (1)

1 imagine [Marne-la-Vallée]

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.

Mots clés: Exploration-exploitation tradeoff; Multi-armed bandits; Risk analysis; deviations

Domaines: Autres [stat.ML]

Antoine Salomon, Jean-Yves Audibert. Robustness of Anytime Bandit Policies. 2011. ⟨hal-00579607v2⟩