Bayesian Optimization (BO) links Gaussian Process (GP) surrogates with sequential design toward optimizing expensive-to-evaluate black-box functions. Example design heuristics, or so-called acquisition functions, like expected improvement (EI), balance exploration and exploitation to furnish global solutions under stringent evaluation budgets. However, they fall short when solving for robust optima, meaning a preference for solutions in a wider domain of attraction. Robust solutions are useful when inputs are imprecisely specified, or where a series of solutions is desired. A common mathematical programming technique in such settings involves an adversarial objective, biasing a local solver away from ``sharp'' troughs. Here we propose a surrogate modeling and active learning technique called robust expected improvement (REI) that ports adversarial methodology into the BO/GP framework. After describing the methods, we illustrate and draw comparisons to several competitors on benchmark synthetic and real problems of varying complexity.

翻译：贝叶斯优化（BO）将高斯过程（GP）代理模型与序贯设计相结合，旨在优化评估代价高昂的黑箱函数。典型的设计启发式方法（即所谓采集函数），如期望改进（EI），通过平衡探索与利用，在严格的评估预算下求解全局最优解。然而，这些方法在求解鲁棒最优解时存在不足——即偏好具有更宽吸引域的解。当输入参数存在不精确指定或需要一系列解时，鲁棒解尤其具有实用价值。此类问题中常见的数学规划技术涉及对抗性目标函数，通过引导局部优化器远离"尖锐"低谷来获得鲁棒解。本文提出一种称为鲁棒期望改进（REI）的代理建模与主动学习方法，将对抗性方法论移植至BO/GP框架中。在阐述该方法后，我们通过不同复杂度的基准合成问题与实际问题，与多种竞争方法进行了对比验证。