SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 3, Page 891-925, January 2020.
Design of systems based on computer simulations is prevalent. An important idea to improve design quality, called robust parameter design (RPD), is to optimize control factors based on the expectation of a loss function so that the design is robust to noise factor variations. When computer simulations are time consuming, optimizing the simulator based on a Gaussian process (GP) emulator for the response is a computationally efficient approach. For this purpose, acquisition functions (AFs) are used to sequentially determine the next design point so that the GP emulator can more accurately locate the optimal setting. Despite this, few articles consider AFs for positive definite quadratic forms such as the expected quadratic loss (EQL) function, which is the standard expected loss function for RPD with nominally-the-best responses. This paper proposes new AFs for optimizing the EQL, analyzes their convergence, and develops quick and accurate methods based on the characteristic function of the EQL to compute them. We apply the AFs to RPD problems with internal noise factors based on a GP model and an initial design tailored for such problems. Numerical results indicate that all four AFs considered have similar performance, and they outperform an optimization approach based on modeling the quadratic loss as a GP and maximin Latin hypercube designs. MATLAB codes for reproducing reported results are given in the online supplement.

中文翻译：

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具有内部噪声的多响应计算机实验的预期二次损失的贝叶斯优化

SIAM / ASA不确定性量化期刊，第8卷，第3期，第891-925页，2020年1月。
基于计算机仿真的系统设计是普遍的。改善设计质量的一个重要想法是鲁棒参数设计（RPD），它是基于对损耗函数的期望来优化控制因子的，从而使设计对于噪声因子的变化具有鲁棒性。当计算机模拟非常耗时时，基于高斯过程（GP）仿真器针对响应进行优化是一种计算有效的方法。为此，可以使用采集功能（AF）顺序确定下一个设计点，以便GP仿真器可以更准确地定位最佳设置。尽管如此，很少有文章考虑将AF用于正定二次形式，例如预期二次损失（EQL）函数，这是具有最佳响应的RPD的标准预期损失函数。本文提出了用于优化EQL的新AF，分析了它们的收敛性，并根据EQL的特征函数开发了快速准确的方法来进行计算。我们基于GP模型和针对此类问题量身定制的初始设计，将AF应用于具有内部噪声因子的RPD问题。数值结果表明，所考虑的所有四个AF具有相似的性能，并且它们优于基于将GP和maximin拉丁超立方体设计建模为二次损失的优化方法。在线补充资料中提供了用于再现报告结果的MATLAB代码。我们基于GP模型和针对此类问题量身定制的初始设计，将AF应用于具有内部噪声因子的RPD问题。数值结果表明，所考虑的所有四个AF具有相似的性能，并且它们优于基于将GP和maximin拉丁超立方体设计建模为二次损失的优化方法。在线补充资料中提供了用于再现报告结果的MATLAB代码。我们基于GP模型和针对此类问题量身定制的初始设计，将AF应用于具有内部噪声因子的RPD问题。数值结果表明，所考虑的所有四个AF都具有相似的性能，并且它们优于基于将二次损失建模为GP和maximin Latin hypercube设计的优化方法。在线补充资料中提供了用于再现报告结果的MATLAB代码。