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

Sébastien Bubeck, Damien Ernst, Aurélien Garivier; 14(Feb):601−623, 2013.

Abstract

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.

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