  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.
