Learning efficient representations of complex constraints for scalable optimization

Abstract: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.

Machine Learning (cs.LG); Systems and Control (eess.SY); Optimization and Control (math.OC)

arXiv:2603.08283 [cs.LG]

(or arXiv:2603.08283v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2603.08283 Focus to learn more arXiv-issued DOI via DataCite

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