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

Context: 
CIRM, Rencontres de Statistique Mathématique "Mathematical Statistics with Applications in Mind"
Resume: 

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.

Slides: 
Date: 
December, 2013