Bayesian Optimization with Inequality Constraints

TLDR

Bayesian optimization efficiently minimizes expensive objective functions with few evaluations and has been applied to hyperparameter tuning and experimental design, but it has not yet been extended to inequality‑constrained settings where feasibility checks are as costly as objective evaluations. The study introduces constrained Bayesian optimization, placing prior distributions on both objective and constraint functions. The approach models both objective and constraint functions with prior distributions and is evaluated on simulated and real datasets. On simulated and real data, constrained Bayesian optimization quickly finds optimal and feasible points, outperforming standard methods when feasible regions are small.

Abstract

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 problems, including hyperparameter tuning and experimental 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 constrained 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 constrained Bayesian optimization can quickly find optimal and feasible points, even when small feasible regions cause standard methods to fail.