Best of both worlds: Stochastic & adversarial best-arm identification
Abstract
We study bandit best-arm identification with arbitrary and potentially adversarial rewards. A simple random uniform learner obtains the optimal rate of error in the adversarial scenario. However, this type of strategy is suboptimal when the rewards are sampled stochastically. Therefore, we ask: Can we design a learner that performs optimally in both the stochastic and adversarial problems while not being aware of the nature of the rewards? First, we show that designing such a learner is impossible in general. In particular, to be robust to adversarial rewards, we can only guarantee optimal rates of error on a subset of the stochastic problems. We give a lower bound that characterizes the optimal rate in stochastic problems if the strategy is constrained to be robust to adversarial rewards. Finally, we design a simple parameter-free algorithm and show that its probability of error matches (up to log factors) the lower bound in stochastic problems, and it is also robust to adversarial ones.
Cite
@article{arxiv.2604.14860,
title = {Best of both worlds: Stochastic & adversarial best-arm identification},
author = {Yasin Abbasi-Yadkori and Peter L. Bartlett and Victor Gabillon and Alan Malek and Michal Valko},
journal= {arXiv preprint arXiv:2604.14860},
year = {2026}
}
Comments
Published in Conference on Learning Theory (COLT 2018)