Tracking Most Significant Shifts in Nonparametric Contextual Bandits

TL;DR

This paper investigates nonparametric contextual bandits with changing reward functions, establishing minimax regret bounds based on the number of changes and proposing a local, significance-based change measure for better adaptivity.

Contribution

It introduces a new notion of experienced significant shifts that accounts for local and impactful changes, enabling adaptive algorithms without prior knowledge of change parameters.

Findings

Established minimax dynamic regret rates in nonparametric contextual bandits.

Proposed a locality-aware change measure called experienced significant shifts.

Showed that adaptive algorithms can achieve minimax rates using this new change measure.

Abstract

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.