Hedging under uncertainty: regret minimization meets exponentially fast convergence

Johanne Cohen 1 Amélie Héliou 2, 3, 4 Panayotis Mertikopoulos 5
2 AMIB - Algorithms and Models for Integrative Biology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France
5 POLARIS - Performance analysis and optimization of LARge Infrastructures and Systems
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
Abstract : This paper examines the problem of multi-agent learning in N-person non-cooperative games. For concreteness, we focus on the so-called “hedge” variant of the exponential weights (EW) algorithm, one of the most widely studied algorithmic schemes for regret minimization in online learning. In this multi-agent context, we show that a) dominated strategies become extinct (a.s.); and b) in generic games, pure Nash equilibria are attracting with high probability, even in the presence of uncertainty and noise of arbitrarily high variance. Moreover, if the algorithm’s step-size does not decay too fast, we show that these properties occur at a quasi-exponential rate – that is, much faster than the algorithm’s O(1/\sqrt{T}) worst-case regret guarantee would suggest.
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Conference papers
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Contributor : Panayotis Mertikopoulos <>
Submitted on : Sunday, October 16, 2016 - 3:29:10 PM
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Johanne Cohen, Amélie Héliou, Panayotis Mertikopoulos. Hedging under uncertainty: regret minimization meets exponentially fast convergence. Symposium on Algorithmic Game Theory (SAGT) 2017, Sep 2017, L'Aquila, Italy. ⟨10.1007/978-3-319-66700-3_20⟩. ⟨hal-01382290⟩



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