Knowledge Gradient for Selection with Covariates: Consistency and Computation
Knowledge Gradient for Selection with Covariates: Consistency and Computation
复制标题
协变量选择的知识梯度：一致性和计算
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Xiaowei Zhang
中科院分区：
文献类型：
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作者：
Liang Ding;L. Hong;Haihui Shen;Xiaowei Zhang
知识梯度是贝叶斯序贯抽样策略的设计原则，本文考虑协变量存在时的排序和选择问题，其中最佳方案不是普适的，而是依赖于协变量。在这种情况下，我们证明，在最小的假设下，基于知识梯度的抽样政策是一致的，在这个意义上，以下的政策作为协变量的函数的最佳选择将被确定几乎粗暴的样本数量的增长。我们还提出了一个随机梯度上升算法计算的采样策略，并通过数值实验证明其性能。
Knowledge gradient is a design principle for developing Bayesian sequential sampling policies to consider in this paper the ranking and selection problem in the presence of covariates, where the best alternative is not universal but depends on the covariates. In this context, we prove that under minimal assumptions, the sampling policy based on knowledge gradient is consistent, in the sense that following the policy the best alternative as a function of the covariates will be identified almost surly as the number of samples grows. We also propose a stochastic gradient ascent algorithm for computing the sampling policy and demonstrate its performance via numerical experiments.