Exploration-exploitation tradeoff using variance estimates in multi-armed bandits
Theoretical Computer Science
Active learning with statistical models
Journal of Artificial Intelligence Research
Active learning in heteroscedastic noise
Theoretical Computer Science
Pure exploration in finitely-armed and continuous-armed bandits
Theoretical Computer Science
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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.