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 $O(sqrt{TA Upsilon_Tlog(T)})$ 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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