Gambling in a rigged casino: The adversarial multi-armed bandit problem

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Gambling in a rigged casino: The adversarial multi-armed bandit problem (1995)

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by Peter Auer , Nicolò Cesa-Bianchi , Yoav Freund , Robert E. Schapire

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241 - 8 self

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@MISC{Auer95gamblingin,
    author = {Peter Auer and Nicolò Cesa-Bianchi and Yoav Freund and Robert E. Schapire},
    title = {Gambling in a rigged casino: The adversarial multi-armed bandit problem},
    year = {1995}
}

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Abstract

In the multi-armed bandit problem, a gambler must decide which arm of K non-identical slot machines to play in a sequence of trials so as to maximize his reward. This classical problem has received much attention because of the simple model it provides of the trade-off between exploration (trying out each arm to find the best one) and exploitation (playing the arm believed to give the best payoff). Past solutions for the bandit problem have almost always relied on assumptions about the statistics of the slot machines. In this work, we make no statistical assumptions whatsoever about the nature of the process generating the payoffs of the slot machines. We give a solution to the bandit problem in which an adversary, rather than a well-behaved stochastic process, has complete control over the payoffs. In a sequence of T plays, we prove that the expected per-round payoff of our algorithm approaches that of the best arm at the rate O(T \Gamma1=2 ), and we give an improved rate of conver...

Keyphrases

adversarial multi-armed bandit problem rigged casino bandit problem slot machine simple model improved rate non-identical slot machine complete control well-behaved stochastic process past solution multi-armed bandit problem statistical assumption classical problem expected per-round payoff much attention

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