Ecole d'ingénieur et centre de recherche en Sciences du numérique

Regret-optimal strategies for playing repeated games with discounted losses

Kamble, Vijay; Loiseau, Patrick; Walrand, Jean

Technical report submitted on ArXiv, March 16, 2016

The regret-minimization paradigm has emerged as a powerful technique for designing algorithms for online decision-making in adversarial environments. But so far, designing exact minmax-optimal algorithms for minimizing the worst-case regret has proven to be a dicult task in general, with only a few known results in speci c settings. In this paper, we present a novel set-valued dynamic programming approach for designing such exact regret-optimal policies for playing repeated games with discounted losses. Our approach first draws the connection between regret minimization, and determining minimal achievable guarantees in repeated games with vector-valued losses. We then characterize the set of these minimal guarantees as the xed point of a dynamic programming operator de ned on the space of Pareto frontiers of convex and compact sets. This approach simultaneously results in the characterization of the optimal strategies that achieve these minimal guarantees, and hence of regret-optimal strategies in the original repeated game. As an illustration of our approach, we design a simple near-optimal strategy for prediction using expert advice for the case of 2 experts

Arxiv Bibtex

Titre:Regret-optimal strategies for playing repeated games with discounted losses
Type:Rapport
Langue:English
Ville:
Date:
Département:Data Science
Eurecom ref:4853
Copyright: © EURECOM. Personal use of this material is permitted. The definitive version of this paper was published in Technical report submitted on ArXiv, March 16, 2016 and is available at :
Bibtex: @techreport{EURECOM+4853, year = {2016}, title = {{R}egret-optimal strategies for playing repeated games with discounted losses}, author = {{K}amble, {V}ijay and {L}oiseau, {P}atrick and {W}alrand, {J}ean }, number = {EURECOM+4853}, month = {03}, institution = {Eurecom}, url = {http://www.eurecom.fr/publication/4853},, }
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