AI 中文总结
该研究针对灰盒优化问题，提出双层贝叶斯优化方法，通过外层优化黑盒变量、内层求解白盒子问题，在13个基准问题上实现更低后悔值，且优势具有鲁棒性。
AI 中文摘要
我们研究灰盒优化问题，其中决策变量自然分为黑盒变量（作为昂贵黑盒函数的参数）和白盒变量，白盒变量由一组显式闭式方程控制，且这些方程也依赖于黑盒函数的输出。我们通过双层重构来利用这种可分性：外层采用贝叶斯优化（BO）仅针对黑盒变量优化标量目标，内层问题通过全局优化求解白盒子问题。因此，BO中使用的高斯过程替代模型被明确界定，且只要内层优化器收敛到可行点，白盒约束就会精确满足——无需惩罚函数、机会约束或矩近似。在13个基准问题套件上，双层BO实现了更低的后悔值，且迭代次数和挂钟时间更少。这种优势对初始化集大小、探索参数和内层求解器的选择具有鲁棒性。
英文摘要
We consider grey-box optimization problems where the decision variables naturally partition into black-box variables (as arguments to an expensive black-box function) and white-box variables, governed by a set of explicit, closed-form equations that also depend on the output of the black-box function. We exploit this separability through a bilevel reformulation: an outer Bayesian optimization (BO) to optimize the scalar objective as a function of black-box variables alone, while an inner problem solves the white-box subproblem via global optimization. The Gaussian process surrogate used in BO is therefore defined rather than and white-box constraints are satisfied exactly whenever the inner optimizer converges to a feasible point---without penalty functions, chance constraints, or moment approximations. On a suite of 13 benchmark problems, bilevel BO achieves lower regret, with fewer iterations and wall clock time. This advantage is robust to initialization set size, exploration parameters, and inner-solver choice.
