# COBALT: COnstrained Bayesian optimizAtion of computationaLly expensive grey-box models exploiting derivaTive information

arXiv: https://arxiv.org/abs/2105.04114 · HTML: https://mlsanity.com/paper/2105.04114/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2021.

## Built on by (most cited first, 16 of 16)

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- [Bayesian Optimization of Partially Known Systems using Hybrid Models](https://mlsanity.com/paper/2603.11199/) (2026)
- [An Efficient Spatial Branch-and-Bound Algorithm for Global Optimization of Gaussian Process Posterior Mean Functions](https://mlsanity.com/paper/2605.00855/) (2026)
- [A Human-in-the-Loop Bayesian Optimization Framework for Constraint-Aware Bioprocess Development](https://mlsanity.com/paper/2606.19230/) (2026)
- [Exploiting Separability in Multi-Scale Grey-Box Bayesian Optimization](https://mlsanity.com/paper/2608.03045/) (2026)
- [Atoms to Processes: The Role of Artificial Intelligence and Machine Learning in Chemical Engineering](https://mlsanity.com/paper/2610.02014/) (2026)

## Abstract (arXiv)

Many engineering problems involve the optimization of computationally expensive models for which derivative information is not readily available. The Bayesian optimization (BO) framework is a particularly promising approach for solving these problems, which uses Gaussian process (GP) models and an expected utility function to systematically tradeoff between exploitation and exploration of the design space. BO, however, is fundamentally limited by the black-box model assumption that does not take into account any underlying problem structure. In this paper, we propose a new algorithm, COBALT, for constrained grey-box optimization problems that combines multivariate GP models with a novel constrained expected utility function whose structure can be exploited by state-of-the-art nonlinear programming solvers. COBALT is compared to traditional BO on seven test problems including the calibration of a genome-scale bioreactor model to experimental data. Overall, COBALT shows very promising performance on both unconstrained and constrained test problems.