Learning efficient representations of complex constraints for scalable optimization

Complex constraints often make real-world optimization computationally prohibitive at the scale and speed required for operational decision-making. Here we introduce PolyFormer, a PIML framework that learns compact polytopic representations of the geometry induced by complex constraints. PolyFormer captures constraint-induced geometry and transforms it into efficient polytopic reformulations, reducing the complexity of downstream optimization and enabling the use of off-the-shelf solvers. Neural parameterizations further enable rapid adaptation to varying operating conditions without retraining. Through evaluations across three important problems, i.e., large-scale resource aggregation, network-constrained optimization, and optimization under uncertainty, PolyFormer achieves online solver speedups of up to 6,400-fold and memory reductions of up to 99.87%, while maintaining small feasibility and objective errors. Together, these results establish learned geometric constraint representations as an effective and scalable route to prescriptive optimization under diverse forms of constraint complexity.