Optimal learning for sequential sampling with non-parametric beliefs

被引:5
作者
Barut, Emre [1 ]
Powell, Warren B. [1 ]
机构
[1] Princeton Univ, Dept Operat Res & Financial Engn, Princeton, NJ 08544 USA
关键词
Bayesian global optimization; Knowledge gradient; Non-parametric estimation; GLOBAL OPTIMIZATION; KNOWLEDGE-GRADIENT; APPROXIMATION; AGGREGATION; SELECTION;
D O I
10.1007/s10898-013-0050-5
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
We propose a sequential learning policy for ranking and selection problems, where we use a non-parametric procedure for estimating the value of a policy. Our estimation approach aggregates over a set of kernel functions in order to achieve a more consistent estimator. Each element in the kernel estimation set uses a different bandwidth to achieve better aggregation. The final estimate uses a weighting scheme with the inverse mean square errors of the kernel estimators as weights. This weighting scheme is shown to be optimal under independent kernel estimators. For choosing the measurement, we employ the knowledge gradient policy that relies on predictive distributions to calculate the optimal sampling point. Our method allows a setting where the beliefs are expected to be correlated but the correlation structure is unknown beforehand. Moreover, the proposed policy is shown to be asymptotically optimal.
引用
收藏
页码:517 / 543
页数:27
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