A feasible region is the subset of the search space containing inputs that satisfy every optimization constraint. With a cost constraint, a point is feasible when its cost is nonpositive. section 8.1.2
In black-box optimization, the feasible region is not known in advance. Querying a candidate reveals both its objective value and constraint costs, while Gaussian-process models estimate where future candidates are likely to be feasible. section 8.1.2
Constraint-aware search proceeds by:
- Modeling the objective and each constraint-defining function with separate Gaussian processes. section 8.1.2
- Balancing objective improvement with the probability that a candidate lies in the feasible region. section 8.4
- Updating the models after querying both the objective and constraint functions. section 8.1.2
A one-dimensional constrained search
A search over bounds from -5 to 5 evaluates an objective and a cost function. Constrained expected improvement favors candidates that improve the objective while satisfying cost ≤ 0, finding better feasible solutions on average than regular expected improvement.
