## Regret minimization under partial monitoring (2004)

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Venue: | MATHEMATICS OF OPERATIONS RESEARCH |

Citations: | 33 - 7 self |

### BibTeX

@ARTICLE{Cesa-Bianchi04regretminimization,

author = {Nicolò Cesa-Bianchi and Gábor Lugosi and Gilles Stoltz},

title = {Regret minimization under partial monitoring},

journal = {MATHEMATICS OF OPERATIONS RESEARCH},

year = {2004},

volume = {31},

pages = {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 this 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) on the convergence rate of the regret, and exhibit a specific strategy that attains this rate on any game for which a Hannan consistent player exists.