Efficient Change-Point Detection for Tackling Piecewise-Stationary Bandits

Lilian Besson; Emilie Kaufmann; Odalric-Ambrym Maillard; Julien Seznec

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arXiv · 1902.01575

Efficient Change-Point Detection for Tackling Piecewise-Stationary Bandits

Lilian Besson·Emilie Kaufmann·Odalric-Ambrym Maillard·Julien Seznec

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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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Lilian Besson, Emilie Kaufmann, Odalric-Ambrym Maillard, Julien Seznec. 2019-02-05. Efficient Change-Point Detection for Tackling Piecewise-Stationary Bandits. https://arxiv.org/abs/1902.01575

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