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.
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Chen, KY., Lin, CT. A note on strategies for bandit problems with infinitely many arms. Metrika 59, 193–203 (2004). https://doi.org/10.1007/s001840300279
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DOI: https://doi.org/10.1007/s001840300279