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This paper investigates the problem of best arm identification in$\textit{contaminated}$ stochastic multi-arm bandits. In this setting, therewards obtained from any arm are replaced by samples from an adversarial modelwith probability $\varepsilon$. A fixed confidence (infinite-horizon) settingis considered, where the goal of the learner is to identify the arm with thelargest mean. Owing to the adversarial contamination of the rewards, each arm'smean is only partially identifiable. This paper proposes two algorithms, agap-based algorithm and one based on the successive elimination, for best armidentification in sub-Gaussian bandits. These algorithms involve mean estimatesthat achieve the optimal error guarantee on the deviation of the true mean fromthe estimate asymptotically. Furthermore, these algorithms asymptoticallyachieve the optimal sample complexity. Specifically, for the gap-basedalgorithm, the sample complexity is asymptotically optimal up to constantfactors, while for the successive elimination-based algorithm, it is optimal upto logarithmic factors. Finally, numerical experiments are provided toillustrate the gains of the algorithms compared to the existing baselines.

Mean-based Best Arm Identification in Stochastic Bandits under Reward Contamination