Regret Minimization Under Partial Monitoring

  • Authors:
  • Nicolò Cesa-Bianchi;Gábor Lugosi;Gilles Stoltz

  • Affiliations:
  • Dipartimento de Scienze dell' Informazione, Università di Milano, Milano, Italy;ICREA and Department of Economics, Pompeu Fabra University, Barcelona, Spain;CNRS and Département de Mathématiques et Applications, Ecole Normale Supérieure, Paris, France

  • Venue:
  • Mathematics of Operations Research
  • Year:
  • 2006

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Abstract

We consider repeated games in which the player, instead of observing the action chosen by the opponent in each game round, receives a feedback generated by the combined choice of the two players. We study Hannan-consistent players for these games, that is, randomized playing strategies whose per-round regret vanishes with probability one as the number n of game rounds goes to infinity. We prove a general lower bound of Ω(n-1/3) for the convergence rate of the regret, and exhibit a specific strategy that attains this rate for any game for which a Hannan-consistent player exists.