Exploiting Separability in Multi-Scale Grey-Box Bayesian Optimization

2026-08-03

AI Summary

This work addresses the high computational cost and constraint-handling challenges in gray-box optimization arising from the coupling between black-box and white-box variables. To this end, it proposes a bilevel decomposition approach that exploits variable separability: the outer loop employs Bayesian optimization to optimize only the black-box variables, while the inner loop solves the white-box subproblem to global optimality using deterministic global optimization. Notably, this method is the first in gray-box Bayesian optimization to rigorously enforce white-box constraints without resorting to penalty functions, chance constraints, or moment approximations, thereby significantly enhancing both efficiency and robustness. Empirical results across 13 benchmark problems demonstrate that the proposed approach achieves lower regret with fewer iterations and less runtime, while exhibiting strong robustness to variations in initialization size, exploration parameters, and choice of inner-loop solver.

Abstract

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.

Problem

• grey-box optimization
• black-box variables
• white-box variables
• separability
• Bayesian optimization

Innovation

• grey-box optimization
• separability
• bilevel Bayesian optimization
• white-box constraints
• Gaussian process surrogate