Efficient Change-Point Detection for Tackling Piecewise-Stationary Bandits

Lilian Besson (1) , Emilie Kaufmann (2) , Odalric-Ambrym Maillard (2) , Julien Seznec (2, 3)

1 ENS Rennes - École normale supérieure - Rennes
2 Scool - Scool
3 Lelivrescolaire.fr

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.

Mots clés: Multi-Armed Bandits; Non-Stationary Bandits; Change Point Detection

Domaines: Autres [stat.ML]

Lilian Besson, Emilie Kaufmann, Odalric-Ambrym Maillard, Julien Seznec. Efficient Change-Point Detection for Tackling Piecewise-Stationary Bandits. Journal of Machine Learning Research, 2022. ⟨hal-02006471v3⟩