A constraint function determines whether a candidate satisfies an optimization constraint. In constrained Bayesian optimization, its value can represent a cost that must remain nonpositive; feasible candidates satisfy the specified bounds. section 8.1.2
When the constraint function is a black box, its values are observed only at queried points. A separate Gaussian process models each constraint function, allowing the optimizer to estimate the probability that a new point is feasible rather than assuming the feasible region is known. section 8.1.2 section 8.6
A constraint-aware optimization loop uses constraint functions to:
- Train one Gaussian process on the observed values of each constraint function. section 8.1.2
- Estimate each candidate's probability of feasibility from the predictive distribution. section 8.6
- Combine feasibility with objective improvement by incorporating that probability into constrained expected improvement. section 8.6
