A New Knowledge Gradient-based Method for Constrained Bayesian Optimization
This work addresses optimization challenges in domains like structural design and drug experiments, but it appears incremental as it builds on existing knowledge gradient methods for constrained settings.
The paper tackles constrained black-box optimization problems with expensive and noisy evaluations by developing a novel Bayesian optimization approach based on the knowledge gradient method, proposing a new acquisition function for batch sampling that balances optimality and feasibility.
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.