Best Arm Identification for Bandits with Shifting Means
We study the best arm identification problem in a stochastic environment with a novel form of adversarial perturbations, which we coin Shifting Means. While classically the mean rewards of the $K$ arms are stable in time, in Shifting Means only the gaps $\boldsymbolΔ$ between mean rewards are stable, while their common shift may be determined adversarially in each round. The objective of the learner is to identify the best arm with high probability while minimizing sample complexity (the fixed confidence setting). Handling shifts requires new tools: we show that algorithms employing a Generalized Likelihood Ratio Test (GLRT) stopping rule, including the popular Track-and-Stop, fail under ...
| Authors | Lukas Zierahn, Wouter M. Koolen, Shubhada Agrawal et al. |
|---|---|
| Primary category | stat.ML |
| Published | 7 October 2026 |
| Last updated at source | 7 October 2026 |
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