Bayesian Optimization with Inequality Constraints

Bayesian optimization is a powerful frame-work for minimizing expensive objective functions while using very few function eval-uations. It has been successfully applied to a variety of problems, including hyperparam-eter tuning and experimental design. How-ever, this framework has not been extended to the inequality-constrained optimization setting, particularly the setting in which eval-uating feasibility is just as expensive as eval-uating the objective. Here we present con-strained Bayesian optimization, which places a prior distribution on both the objective and the constraint functions. We evaluate our method on simulated and real data, demon-strating that constrained Bayesian optimiza-tion can quickly find optimal and feasible points, even when small feasible regions cause standard methods to fail. 1