Generalized Linear Bandits (GLBs) are powerful extensions to the Linear
Bandit (LB) setting, broadening the benefits of reward parametrization beyond
linearity. In this paper we study GLBs in non-stationary environments,
characterized by a general metric of non-stationarity known as the
variation-budget or \emph{parameter-drift}, denoted $B_T$. While previous
attempts have been made to extend LB algorithms to this setting, they overlook
a salient feature of GLBs which flaws their results. In this work, we introduce
a new algorithm that addresses this difficulty. We prove that under a geometric
assumption on the action set, our approach enjoys a
$\tilde{\mathcal{O}}(B_T^{1/3}T^{2/3})$ regret bound. In the general case, we
show 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 step
introduced in Filippi et al. (2010), adapted to the non-stationary nature of
the problem. Our analysis sheds light on central mechanisms inherited from the
setting by explicitly splitting the treatment of the learning and tracking
aspects of the problem.

本文探究了广义线性 Bandits 在非稳态环境中的应用，比如参数漂移等问题，提出了一种新增添的算法，基于动态问题的推断，解决了广义线性 Bandits 在非稳态环境下表现出的缺陷，拥有了更优秀的性能表现。通过对于动态问题投影过程的修改，我们设计出了一种具有结构性特点的算法。经过实验证明，我们的算法达到了更好的性能表现。