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 exercises and real problems of varying complexity.

翻译：贝叶斯优化（BO）将高斯过程（GP）代理模型与序列设计相结合，用于优化评估代价昂贵的黑箱函数。期望改进（EI）等典型设计启发式方法（即所谓的采集函数）通过平衡探索与利用，在严格评估预算下获得全局解。然而，当求解鲁棒最优解时——即偏好处于更广吸引域内的解——这些方法存在不足。鲁棒解在输入不精确或需要一系列解的场景中具有重要价值。此类情境下，一种常见的数学规划技术涉及对抗目标函数，使局部求解器偏离"尖锐"谷底。本文提出一种名为鲁棒期望改进（REI）的代理建模与主动学习方法，将对抗性方法论引入BO/GP框架。在方法描述之后，我们通过标准合成测试问题及不同复杂度的实际案例展示结果，并与若干竞争方法进行对比分析。