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KL-UCB-switch: optimal regret bounds for stochastic bandits from both a distribution-dependent and a distribution-free viewpoints

Abstract

In the context of K-armed stochastic bandits with distribution only assumed to be supported by [0,1], we introduce the first algorithm, called KL-UCB-switch, that enjoys simultaneously a distribution-free regret bound of optimal order $\sqrt{KT}$ and a distribution-dependent regret bound of optimal order as well, that is, matching the $\kappa\ln T$ lower bound by Lai & Robbins (1985) and Burnetas & Katehakis (1996). This self-contained contribution simultaneously presents state-of-the-art techniques for regret minimization in bandit models, and an elementary construction of non-asymptotic confidence bounds based on the empirical likelihood method for bounded distributions.
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Dates and versions

hal-01785705 , version 1 (04-05-2018)
hal-01785705 , version 2 (05-11-2019)
hal-01785705 , version 3 (28-06-2022)

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Aurélien Garivier, Hédi Hadiji, Pierre Ménard, Gilles Stoltz. KL-UCB-switch: optimal regret bounds for stochastic bandits from both a distribution-dependent and a distribution-free viewpoints. 2019. ⟨hal-01785705v2⟩
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