Regret minimization under partial monitoring
Nicolò Cesa-Bianchi, Gábor Lugosi and Gilles Stoltz
Submitted 2004.

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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 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.

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