Selection of the Most Probable Best Under Input Uncertainty
Selection of the Most Probable Best Under Input Uncertainty
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DOI：
10.1109/wsc52266.2021.9715474
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发表时间：
2021-12
期刊：
影响因子：
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通讯作者：
K. Kim;Taeho Kim;Eunhye Song
中科院分区：
文献类型：
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作者：
K. Kim;Taeho Kim;Eunhye Song
我们考虑的排名和选择问题，其配置依赖于一个共同的输入模型估计从有限的现实世界的观察。为了找到一个对输入模型中的估计误差具有鲁棒性的解，我们引入了一个新的鲁棒最优性概念：最可能最优。从贝叶斯的观点来看，最可能的最佳解被定义为在给定真实世界数据的情况下，其最佳解的后验概率最大的解。针对输入模型的后验具有有限支持度的情况，研究了错误选择最可能最优值的概率的大偏差率，并给出了该问题的最优计算预算分配（OCBA）方案.我们进一步近似OCBA问题，以获得一个简单的和可解释的预算分配规则，并提出顺序学习算法。数值研究表明，所提出的算法具有良好的性能。
We consider a ranking and selection problem whose configuration depends on a common input model estimated from finite real-world observations. To find a solution robust to estimation error in the input model, we introduce a new concept of robust optimality: the most probable best. Taking the Bayesian view, the most probable best is defined as the solution whose posterior probability of being the best is the largest given the real-world data. Focusing on the case where the posterior on the input model has finite support, we study the large deviation rate of the probability of incorrectly selecting the most probable best and formulate an optimal computing budget allocation (OCBA) scheme for this problem. We further approximate the OCBA problem to obtain a simple and interpretable budget allocation rule and propose sequential learning algorithms. A numerical study demonstrates good performances of the proposed algorithms.