PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Best arm identification in multi-armed bandits
Jean-Yves Audibert, Sébastien Bubeck and Rémi Munos
In: COLT 2010, Israel(2010).

Abstract

We consider the problem of finding the best arm in a stochastic multi-armed bandit game. The regret of a forecaster is here defined by the gap between the mean reward of the optimal arm and the mean reward of the ultimately chosen arm. We propose a highly exploring UCB policy and a new algorithm based on successive rejects. We show that these algorithms are essentially optimal since their regret decreases exponentially at a rate which is, up to a logarithmic factor, the best possible. However, while the UCB policy needs the tuning of a parameter depending on the unobservable hardness of the task, the successive rejects policy benefits from being parameter-free, and also independent of the scaling of the rewards.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:7409
Deposited By:Rémi Munos
Deposited On:17 March 2011