PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Upper-Confidence-Bound Algorithms for Active Learning in Multi-Armed Bandits
Alexandra Carpentier, Alessandro Lazaric, Mohammad Ghavamzadeh, Remi Munos and Peter Auer
In: Twenty-Second International Conference on Algorithmic Learning Theory (ALT-2011), Espoo, Finland(2011).

Abstract

In this paper, we study the problem of estimating the mean values of all the arms uniformly well in the multi-armed bandit setting. If the variances of the arms were known, one could design an optimal sampling strategy by pulling the arms proportionally to their variances. However, since the distributions are not known in advance, we need to design adaptive sampling strategies to select an arm at each round based on the previous observed samples. We describe two strategies based on pulling the arms proportionally to an upper-bound on their variance and derive regret bounds for these strategies. We show that the performance of these allocation strategies depends not only on the variances of the arms but also on the full shape of their distribution.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
COMPLACS
ID Code:9077
Deposited By:Mohammad Ghavamzadeh
Deposited On:21 February 2012