Some Optimal Strategies for Bandit Problems with Beta Prior Distributions |
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Authors: | Chien-Tai Lin C J Shiau |
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Institution: | (1) Department of Mathematics, Tamkang University, Tamsui, 251, Taiwan R.O.C.;(2) Institute of Mathematical Statistics, National Chung-Cheng University, Chia-Yi, 621, Taiwan R.O.C. |
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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. |
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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 |
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