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Efficient Change-Point Detection for Tackling Piecewise-Stationary Bandits

Abstract : We introduce GLR-klUCB, a novel algorithm for the piecewise iid non-stationary bandit problem with bounded rewards. This algorithm combines an efficient bandit algorithm, kl-UCB, with an efficient, parameter-free, changepoint detector, the Bernoulli Generalized Likelihood Ratio Test, for which we provide new theoretical guarantees of independent interest. Unlike previous non-stationary bandit algorithms using a change-point detector, GLR-klUCB does not need to be calibrated based on prior knowledge on the arms' means. We prove that this algorithm can attain a $O(\sqrt{TA \Upsilon_T\log(T)})$ regret in $T$ rounds on some ``easy'' instances, where A is the number of arms and $\Upsilon_T$ the number of change-points, without prior knowledge of $\Upsilon_T$. In contrast with recently proposed algorithms that are agnostic to $\Upsilon_T$, we perform a numerical study showing that GLR-klUCB is also very efficient in practice, beyond easy instances.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-02006471
Contributor : Emilie Kaufmann <>
Submitted on : Tuesday, December 8, 2020 - 9:26:26 AM
Last modification on : Thursday, January 21, 2021 - 12:12:57 PM

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Distributed under a Creative Commons Attribution - NonCommercial - ShareAlike 4.0 International License

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  • HAL Id : hal-02006471, version 2
  • ARXIV : 1902.01575

Citation

Lilian Besson, Emilie Kaufmann, Odalric-Ambrym Maillard, Julien Seznec. Efficient Change-Point Detection for Tackling Piecewise-Stationary Bandits. 2020. ⟨hal-02006471v2⟩

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