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    Title: Some optimal strategies for bandit problems with beta prior distributions
    Authors: 林千代;Lin, Chien-tai;Shiau, C. J.
    Contributors: 淡江大學數學學系
    Keywords: Bandit problems;sequential experimentation;dynamic allocation of Bernoulli processes;staying-with-a-winner;switching-on-a-loser;k-failure strategy;m-run strategy;non-recalling m-run strategy;N-learning strategy
    Date: 2000-06-01
    Issue Date: 2010-01-28 07:35:53 (UTC+8)
    Publisher: Kluwer Academic Publishers
    Abstract: A bandit problem with infinitely many Bernoulli arms is considered. The parameters of Bernoulli arms are independent and identically distributed random variables from a common distribution with beta(a, b). We investigate the k-failure strategy which is a modification of Robbins's stay-with-a-winner/switch-on-a-loser strategy and three other strategies proposed recently by Berry et al. (1997, Ann. Statist., 25, 2103–2116). We show that the k-failure strategy performs poorly when b is greater than 1, and the best strategy among the k-failure strategies is the 1-failure strategy when b is less than or equal to 1. Utilizing the formulas derived by Berry et al. (1997), we obtain the asymptotic expected failure rates of these three strategies for beta prior distributions. Numerical estimations and simulations for a variety of beta prior distributions are presented to illustrate the performances of these strategies.

    Bandit problemssequential experimentationdynamic allocation of Bernoulli processesstaying-with-a-winnerswitching-on-a-loserk-failure strategym-run strategynon-recalling m-run strategyN-learning strategy
    Relation: Annals of the Institute of Statistical Mathematics 52(2), pp.397-405
    DOI: 10.1023/A:1004130209258
    Appears in Collections:[數學學系暨研究所] 期刊論文

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