KL-UCB-switch: optimal regret bounds for stochastic bandits from both a distribution-dependent and a distribution-free viewpoints
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In the context of K-armed stochastic bandits with distribution only assumed to be supported by [0, 1], we introduce a new algorithm, KL-UCB-switch, and prove that it enjoys simultaneously a distribution-free regret bound of optimal order √(KT) and a distribution-dependent regret bound of optimal order as well, that is, matching the κ T lower bound by Lai and Robbins (1985) and Burnetas and Katehakis (1996).
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