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A note on strategies for bandit problems with infinitely many arms

Author

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  • Kung-Yu Chen
  • Chien-Tai Lin

Abstract

A bandit problem consisting of a sequence of n choices (n→∞) from a number of infinitely many Bernoulli arms is considered. The parameters of Bernoulli arms are independent and identically distributed random variables from a common distribution F on the interval [0,1] and F is continuous with F(0)=0 and F(1)=1. The goal is to investigate the asymptotic expected failure rates of k-failure strategies, and obtain a lower bound for the expected failure proportion over all strategies presented in Berry et al. (1997). We show that the asymptotic expected failure rates of k-failure strategies when 0>b≤1 and a lower bound can be evaluated if the limit of the ratio F(1)−F(t) versus (1−t) b exists as t→1 − for some b>0. Copyright Springer-Verlag 2004

Suggested Citation

  • Kung-Yu Chen & Chien-Tai Lin, 2004. "A note on strategies for bandit problems with infinitely many arms," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(2), pages 193-203, May.
    • Handle: RePEc:spr:metrik:v:59:y:2004:i:2:p:193-203
    DOI: 10.1007/s001840300279
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