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Generalized Linear Bandits (GLBs) are powerful extensions to the LinearBandit (LB) setting, broadening the benefits of reward parametrization beyondlinearity. In this paper we study GLBs in non-stationary environments,characterized by a general metric of non-stationarity known as thevariation-budget or \emph{parameter-drift}, denoted $B_T$. While previousattempts have been made to extend LB algorithms to this setting, they overlooka salient feature of GLBs which flaws their results. In this work, we introducea new algorithm that addresses this difficulty. We prove that under a geometricassumption on the action set, our approach enjoys a$\tilde{\mathcal{O}}(B_T^{1/3}T^{2/3})$ regret bound. In the general case, weshow that it suffers at most a $\tilde{\mathcal{O}}(B_T^{1/5}T^{4/5})$ regret.At the core of our contribution is a generalization of the projection stepintroduced in Filippi et al. (2010), adapted to the non-stationary nature ofthe problem. Our analysis sheds light on central mechanisms inherited from thesetting by explicitly splitting the treatment of the learning and trackingaspects of the problem.

Regret Bounds for Generalized Linear Bandits under Parameter Drift