Optimal discovery with probabilistic expert advice: finite time analysis and macroscopic optimality

Authors:
Sébastien Bubeck;Damien Ernst;Aurélien Garivier
Affiliations:
Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ;Department of Electrical Engineering and Computer Science, University of Liège, Institut Montefiore, Liège, Belgium;Institut de Mathématiques de Toulouse, Toulouse Cedex 9, France
Venue:
The Journal of Machine Learning Research
Year:
2013

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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.