Oct 7, 2026, stat.MLJ/K move · Enter open · S save
Lukas Zierahn, Wouter M. Koolen, Shubhada Agrawal, Christina Katsimerou+1
CWI and Booking.com Science Park 123 1098 XG Amsterdam · CWI and University of Twente Science Park 123 1098 XG Amsterdam · Indian Institute of Science (IISc), Bengaluru CV Raman Rd, Bengaluru, Karnataka 560012, India+2
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
Δ 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 time-varying shifts. Instead, we propose Importance Weights for Shifting Means (
ISM). Assuming means bounded by
U and
σ2-sub-Gaussian rewards, we show
ISM to be
δ-correct and to enjoy a sample complexity bound of order
K(σ2+U2)Δmin−2lnδ1. We also present a matching (up to constant factors) worst-case lower bound and evaluate our results empirically.