用贝叶斯优化解决昂贵黑箱双层优化问题，提升求解效率。
Bayesian Optimization of Bilevel Problems
- 将上下层决策联合建模为高斯过程，实现知识迁移。
- 在多个测试场景中显著减少评估次数，更快找到优质解。
- 适合复杂系统优化，如超参调优与工程设计场景。
双层优化是一种层级数学框架，其中一层优化嵌套于另一层之中，在经济学、工程和机器学习等领域广泛用于建模复杂决策过程。本文聚焦于上下层函数均为昂贵且难以评估的黑箱情形。提出一种贝叶斯优化框架，将上下层函数联合建模为高斯过程，从而在不同子问题间实现知识迁移。此外，设计了一种新颖的采集函数。实验表明，该算法具有极高的样本效率，在寻找高质量解方面优于现有方法。
原文摘要 · Abstract (English)
Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics, engineering, and machine learning. This paper focuses on bilevel optimization where both upper-level and lower-level functions are black boxes and expensive to evaluate. We propose a Bayesian Optimization framework that models the upper and lower-level functions as Gaussian processes over the combined space of upper and lower-level decisions, allowing us to exploit knowledge transfer between different sub-problems. Additionally, we propose a novel acquisition function for this model. Our experimental results demonstrate that the proposed algorithm is highly sample-efficient and outperforms existing methods in finding high-quality solutions.
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