Optimal Discovery with Probabilistic Expert Advice

We consider a variant of a bandit model that arises from some issue of security analysis of a power system. We address it with an optimistic, UCB-type policy using the Good-Turing missing mass estimator. We provide two distincts performance analyses: a "classical" regret bounds under weak assumptions on the probabilistic experts, and a macroscopic optimality result under more restrictive hypotheses. These analyses are illustrated by some numerical experiments.