Finding and Choosing among Multiple Optima

作     者：John Guenther Herbert K. H. Lee Genetha A. Gray 

作者机构：Department of Applied Mathematics and Statistics University of California Santa Cruz USA Quantitative Modeling and Analysis Sandia National Laboratories Livermore USA 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2014年第5卷第2期

页      面：300-317页

学科分类：1002[医学-临床医学] 100214[医学-肿瘤学] 10[医学] 

主　　题：Bayesian Statistics Treed Gaussian Process Emulator Decision Theory Optimization 

摘      要：Black box functions, such as computer experiments, often have multiple optima over the input space of the objective function. While traditional optimization routines focus on finding a single best optimum, we sometimes want to consider the relative merits of multiple optima. First we need a search algorithm that can identify multiple local optima. Then we consider that blindly choosing the global optimum may not always be best. In some cases, the global optimum may not be robust to small deviations in the inputs, which could lead to output values far from the optimum. In those cases, it would be better to choose a slightly less extreme optimum that allows for input deviation with small change in the output;such an optimum would be considered more robust. We use a Bayesian decision theoretic approach to develop a utility function for selecting among multiple optima.