Finding and Choosing among Multiple Optima

• 作者: Genetha A. Gray Herbert K. H. Lee John Guenther
• 来源期刊: 应用数学(英文)
• 学科: 医学
• 关键词: BAYESIAN STATISTICS Treed GAUSSIAN Process EMULATOR DECISION Theory Optimization
• 年，卷（期）: 2014,（2）
• 页码范围: 300-317
• 页数: 18页
• 分类号: R73

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.