We study nonparametric contextual bandits where Lipschitz mean reward functions may change over time. We first establish the minimax dynamic regret rate in this less understood setting in terms of number of changes $L$ and total-variation $V$, both capturing all changes in distribution over context space, and argue that state-of-the-art procedures are suboptimal in this setting. Next, we tend to the question of an adaptivity for this setting, i.e. achieving the minimax rate without knowledge of $L$ or $V$. Quite importantly, we posit that the bandit problem, viewed locally at a given context $X_t$, should not be affected by reward changes in other parts of context space $\cal X$. We therefore propose a notion of change, which we term experienced significant shifts, that better accounts for locality, and thus counts considerably less changes than $L$ and $V$. Furthermore, similar to recent work on non-stationary MAB (Suk & Kpotufe, 2022), experienced significant shifts only count the most significant changes in mean rewards, e.g., severe best-arm changes relevant to observed contexts. Our main result is to show that this more tolerant notion of change can in fact be adapted to.

翻译：我们研究非参数上下文赌博机问题，其中利普希茨均值奖励函数可能随时间变化。首先，在此尚不充分理解的设定下，我们基于变化次数$L$和全变差$V$（两者均捕获上下文空间上分布的所有变化）建立了极小化动态遗憾率，并论证了现有最先进方法在该设定下是次优的。其次，我们探讨该设定的自适应性问题，即在未知$L$或$V$的情况下实现极小化速率。重要的是，我们主张在给定上下文$X_t$的局部视角下，赌博机问题不应受上下文空间$\cal X$其他部分奖励变化的影响。因此，我们提出一种称为“经历显著变化”的新变化概念，它能更好地体现局部性，从而比$L$和$V$统计更少的变化次数。此外，类似于非平稳MAB的最新研究（Suk & Kpotufe, 2022），经历显著变化仅统计均值奖励的最显著变化，例如与观测上下文相关的严重最佳臂切换。我们的主要结果表明，这种更宽容的变化概念实际上是可以实现自适应的。