Bandits Corrupted by Nature: Lower Bounds on Regret and Robust Optimistic Algorithm

Debabrota Basu, Odalric-Ambrym Maillard, Timothée Mathieu

We study the corrupted bandit problem, i.e. a stochastic multi-armed bandit problem with $k$ unknown reward distributions, which are heavy-tailed and corrupted by a history-indepen…