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