提出信息论方法优化双层黑箱函数，同时提升上下层求解效率。
Information-Theoretic Bayesian Optimization for Bilevel Optimization Problems
- 基于信息增益统一衡量上下层优化收益
- 设计可计算的下界评估信息增益，实用性强
- 适合昂贵黑箱函数的双层优化问题
双层优化问题包含嵌套的上下层优化，下层最优解构成上层约束。本文研究上下层均为昂贵黑箱函数时的贝叶斯优化（BO）方法。由于嵌套结构复杂，双层贝叶斯优化远未像多目标或约束优化等标准扩展那样被广泛研究。本文提出一种信息论方法，同时考虑上下层最优解及其取值的信息增益，从而定义统一的优化效益度量准则。此外，还提出了一个实用的下界评估方法来计算信息增益。通过多个基准数据集的实验，验证了所提方法的有效性。
原文摘要 · Abstract (English)
A bilevel optimization problem consists of two optimization problems nested as an upper- and a lower-level problem, in which the optimality of the lower-level problem defines a constraint for the upper-level problem. This paper considers Bayesian optimization (BO) for the case that both the upper- and lower-levels involve expensive black-box functions. Because of its nested structure, bilevel optimization has a complex problem definition, by which bilevel BO has not been widely studied compared with other standard extensions of BO such as multi-objective or constraint problems. We propose an information-theoretic approach that considers the information gain of both the upper- and lower-optimal solutions and values. This enables us to define a unified criterion that measures the benefit for both level problems, simultaneously. Further, we also show a practical lower bound based approach to evaluating the information gain. We empirically demonstrate the effectiveness of our proposed method through several benchmark datasets.
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