caa a22 4500 475826892 CHVBK 20180406123831.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1023/A:1004130209258 doi (NATIONALLICENCE)springer-10.1023/A:1004130209258 Some Optimal Strategies for Bandit Problems with Beta Prior Distributions [Elektronische Daten] [Chien-Tai Lin, C. Shiau] 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. The Institute of Statistical Mathematics, 2000 Bandit problems nationallicence sequential experimentation nationallicence dynamic allocation of Bernoulli processes nationallicence staying-with-a-winner nationallicence switching-on-a-loser nationallicence k -failure strategy nationallicence m -run strategy nationallicence non-recalling m -run strategy nationallicence N -learning strategy nationallicence Lin Chien-Tai Department of Mathematics, Tamkang University, 251, Tamsui, Taiwan R.O.C. aut Shiau C. Institute of Mathematical Statistics, National Chung-Cheng University, 621, Chia-Yi, Taiwan R.O.C. aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/2(2000-06-01), 397-405 0020-3157 52:2<397 2000 52 10463 https://doi.org/10.1023/A:1004130209258 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004130209258 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lin Chien-Tai Department of Mathematics, Tamkang University, 251, Tamsui, Taiwan R.O.C aut NATIONALLICENCE 700 1- Shiau C. Institute of Mathematical Statistics, National Chung-Cheng University, 621, Chia-Yi, Taiwan R.O.C aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/2(2000-06-01), 397-405 0020-3157 52:2<397 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer