利用变量分离性，提升多尺度灰箱优化效率与精度。
Exploiting Separability in Multi-Scale Grey-Box Bayesian Optimization
- 将问题分解为外层贝叶斯优化与内层全局求解器协同优化。
- 在13个基准测试中，以更少迭代次数和时间实现更低遗憾值。
- 无需惩罚函数或近似，可精确满足白箱约束，适合复杂系统设计。
我们研究灰箱优化问题，其中决策变量自然划分为黑箱变量（作为昂贵黑箱函数的输入）和白箱变量，后者由一组显式闭式方程控制，且依赖于黑箱函数的输出。通过双层重构，利用这种分离性：外层贝叶斯优化（BO）仅针对黑箱变量优化标量目标，内层问题则通过全局优化求解白箱子问题。因此，贝叶斯优化中使用的高斯过程代理模型仅定义在黑箱变量上，白箱约束在内层优化器收敛到可行点时被精确满足——无需惩罚函数、概率约束或矩近似。在13个基准问题上，双层贝叶斯优化表现出更低的遗憾值，且迭代次数和实际运行时间更少。该优势对初始化集大小、探索参数和内层求解器选择均具有鲁棒性。
原文摘要 · Abstract (English)
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.
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