Minimax Policy for Heavy-tailed Multi-armed Bandits

07/20/2020

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by   Lai Wei, et al.

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We study the stochastic Multi-Armed Bandit (MAB) problem under worst case regret and heavy-tailed reward distribution. We modify the minimax policy MOSS <cit.> for the sub-Gaussian reward distribution by using saturated empirical mean to design a new algorithm called Robust MOSS. We show that if the moment of order 1+ϵ for the reward distribution exists, then the refined strategy has a worst-case regret matching the lower bound while maintaining a distribution dependent logarithm regret.