Optimal Discovery with Probabilistic Expert Advice: Finite Time Analysis and Macroscopic Optimality

Sébastien Bubeck, Damien Ernst, Aurélien Garivier.

Year: 2013, Volume: 14, Issue: 17, Pages: 601−623


We consider an original problem that arises from the issue of security analysis of a power system and that we name optimal discovery with probabilistic expert advice. We address it with an algorithm based on the optimistic paradigm and on the Good-Turing missing mass estimator. We prove two different regret bounds on the performance of this algorithm under weak assumptions on the probabilistic experts. Under more restrictive hypotheses, we also prove a macroscopic optimality result, comparing the algorithm both with an oracle strategy and with uniform sampling. Finally, we provide numerical experiments illustrating these theoretical findings.