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

TL;DR

COBALT is a new constrained Bayesian optimization algorithm that leverages derivative information in grey-box models to efficiently optimize computationally expensive problems, outperforming traditional black-box BO in tests.

Contribution

The paper introduces COBALT, a constrained Bayesian optimization method that exploits problem structure and derivative information in grey-box models, enhancing optimization efficiency.

Findings

COBALT outperforms traditional BO on test problems.

It effectively handles constrained and unconstrained optimization.

Demonstrates promising results in bioreactor model calibration.

Abstract

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.