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Journal Articles Journal of Machine Learning Research Year : 2023

Adaptation to the Range in $K$-Armed Bandits

Abstract

We consider stochastic bandit problems with $K$ arms, each associated with a bounded distribution supported on the range $[m,M]$. We do not assume that the range $[m,M]$ is known and show that there is a cost for learning this range. Indeed, a new trade-off between distribution-dependent and distribution-free regret bounds arises, which prevents from simultaneously achieving the typical $\ln T$ and $\sqrt{T}$ bounds. For instance, a $\sqrt{T}$}distribution-free regret bound may only be achieved if the distribution-dependent regret bounds are at least of order $\sqrt{T}$. We exhibit a strategy achieving the rates for regret indicated by the new trade-off.
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Dates and versions

hal-02794382 , version 1 (05-06-2020)
hal-02794382 , version 2 (10-11-2020)
hal-02794382 , version 3 (09-06-2022)

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Hédi Hadiji, Gilles Stoltz. Adaptation to the Range in $K$-Armed Bandits. Journal of Machine Learning Research, 2023, 24 (13), pp.1-33. ⟨hal-02794382v3⟩
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