Optimal Bayesian strategies for the infinite-armed Bernoulli bandit |
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Authors: | Ying-Chao Hung |
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Affiliation: | Department of Statistics, National Chengchi University, Taipei 11605, Taiwan |
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Abstract: | We consider the bandit problem with an infinite number of Bernoulli arms, of which the unknown parameters are assumed to be i.i.d. random variables with a common distribution F. Our goal is to construct optimal strategies of choosing “arms” so that the expected long-run failure rate is minimized. We first review a class of strategies and establish their asymptotic properties when F is known. Based on the results, we propose a new strategy and prove that it is asymptotically optimal when F is unknown. Finally, we show that the proposed strategy performs well for a number of simulation scenarios. |
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Keywords: | Bandit problem Bernoulli arms Bayesian strategy Prior distribution |
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