Bayesian Optimization with Inequality Constraints

Bayesian optimization is a powerful framework for minimizing expensive objective functions while using very few function evaluations. It has been successfully applied to a variety of prob-lems, including hyperparameter tuning and ex-perimental design. However, this framework has not been extended to the inequality-constrained optimization setting, particularly the setting in which evaluating feasibility is just as expensive as evaluating 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, demonstrating that con-strained Bayesian optimization can quickly find optimal and feasible points, even when small fea-sible regions cause standard methods to fail. 1