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

arXiv: https://arxiv.org/abs/2608.03045 · HTML: https://mlsanity.com/paper/2608.03045/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 97 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting](https://mlsanity.com/paper/1603.08785/) (2016)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Bayesian Optimization of Composite Functions](https://mlsanity.com/paper/1906.01537/) (2019)
- [Bayesian Optimization of Function Networks](https://mlsanity.com/paper/2112.15311/) (2021)
- [Bayesian optimization under mixed constraints with a slack-variable augmented Lagrangian](https://mlsanity.com/paper/1605.09466/) (2016)
- [COBALT: COnstrained Bayesian optimizAtion of computationaLly expensive grey-box models exploiting derivaTive information](https://mlsanity.com/paper/2105.04114/) (2021)
- [Bayesian Optimization of Function Networks with Partial Evaluations](https://mlsanity.com/paper/2311.02146/) (2023)
- [BONSAI: Structure-exploiting robust Bayesian optimization for networked black-box systems under uncertainty](https://mlsanity.com/paper/2510.03893/) (2025)
- [BOIS: Bayesian Optimization of Interconnected Systems](https://mlsanity.com/paper/2311.11254/) (2023)
- [Bayesian Optimization of Bilevel Problems](https://mlsanity.com/paper/2412.18518/) (2024)
- [BILBO: BILevel Bayesian Optimization](https://mlsanity.com/paper/2502.02121/) (2025)
- [Simulation and optimal control of the Williams-Otto process using Pyomo](https://mlsanity.com/paper/2004.07614/) (2020)

## Abstract (arXiv)

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.