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

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.

Computationally efficient integrated design and predictive control of flexible energy systems using multi‐fidelity simulation‐based Bayesian optimization

“…In addition, it has been recently shown that significant improvements in the convergence rate of BO can be achieved when the cost function can be broken down into a composite function (i.e., f (𝜃) = g(h(𝜃)) where g(⋅) is a known function and h(⋅) is an unknown vector-valued black-box function). 49 It is expected that similar performance gains could be obtained in the multi-fidelity case, if this structure (when present) can somehow be exploited by MF-GP-UCB.…”