Robustness of Anytime Bandit Policies

Antoine Salomon; Jean-Yves Audibert

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arXiv · 1107.4506

Robustness of Anytime Bandit Policies

Antoine Salomon·Jean-Yves Audibert

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Abstract

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.

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Antoine Salomon, Jean-Yves Audibert. 2011-07-25. Robustness of Anytime Bandit Policies. https://arxiv.org/abs/1107.4506

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