A New Knowledge Gradient-based Method for Constrained Bayesian Optimization

TL;DR

This paper introduces a novel constrained Bayesian optimization method based on the knowledge gradient, effectively handling expensive, noisy black-box problems with multiple constraints.

Contribution

It develops a new acquisition function and an unbiased gradient estimator for constrained Bayesian optimization, advancing the state-of-the-art in handling complex black-box problems.

Findings

Effective handling of noisy, expensive black-box evaluations.

New acquisition function improves sample selection for constraints.

Demonstrated superior performance over existing methods.

Abstract

Black-box problems are common in real life like structural design, drug experiments, and machine learning. When optimizing black-box systems, decision-makers always consider multiple performances and give the final decision by comprehensive evaluations. Motivated by such practical needs, we focus on constrained black-box problems where the objective and constraints lack known special structure, and evaluations are expensive and even with noise. We develop a novel constrained Bayesian optimization approach based on the knowledge gradient method ($c-\rm{KG}$). A new acquisition function is proposed to determine the next batch of samples considering optimality and feasibility. An unbiased estimator of the gradient of the new acquisition function is derived to implement the $c-\rm{KG}$ approach.