Exploiting Separability in Multi-Scale Grey-Box Bayesian Optimization
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.