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This research introduces Projection-Adaptive Loss (PAL), a novel training technique that achieves exact constraint satisfaction using a single detached projection step rather than computationally expensive unrolled repair procedures. By adaptively weighting penalties based on the residual after this single step, PAL significantly reduces memory usage and training time while maintaining robustness on highly nonlinear engineering benchmarks. The method represents a critical efficiency advance for deploying learned models in domains where strict feasibility is mandatory, such as power grid optimization and computational finance.
Only Project Once: Projection-Adaptive Loss for Exact Constraint Satisfaction
arXiv:2610.04572v1 Announce Type: cross Abstract: Precise constraint satisfaction is a prerequisite to deploying learned models in many areas, motivating methods that repair raw neural predictions with a repair procedure. Current methods unroll multiple repair steps in training and softly penalize constraint violations that remain after the unroll. This is compute- and memory-intensive, lacks robustness when the repair fails to converge, and surrenders most of the constraint satisfaction work to the repair. Our central finding is that, contrary to common practice, a single detached projection step suffices in training. We accomplish this with a Projection-Adaptive Loss (PAL), which uses the constraint residual after this single step to adaptively weigh constraint penalties on the raw prediction. In experiments, PAL is the only method that retains virtually perfect feasibility on extremely nonlinear constraints, and matches or outperforms current methods on synthetic and engineering benchmarks. Because it only requires a single detached projection step, PAL trains 2.5x faster than the canonical repair-based method (DC3) on its own ACOPF benchmark. PAL can also be trained when constraints are expensive to evaluate (e.g., via neural surrogates), a setting where current unrolled methods are memory-intractable.
Abstract:Precise constraint satisfaction is a prerequisite to deploying learned models in many areas, motivating methods that repair raw neural predictions with a repair procedure. Current methods unroll multiple repair steps in training and softly penalize constraint violations that remain after the unroll. This is compute- and memory-intensive, lacks robustness when the repair fails to converge, and surrenders most of the constraint satisfaction work to the repair. Our central finding is that, contrary to common practice, a single detached projection step suffices in training. We accomplish this with a Projection-Adaptive Loss (PAL), which uses the constraint residual after this single step to adaptively weigh constraint penalties on the raw prediction. In experiments, PAL is the only method that retains virtually perfect feasibility on extremely nonlinear constraints, and matches or outperforms current methods on synthetic and engineering benchmarks. Because it only requires a single detached projection step, PAL trains 2.5x faster than the canonical repair-based method (DC3) on its own ACOPF benchmark. PAL can also be trained when constraints are expensive to evaluate (e.g., via neural surrogates), a setting where current unrolled methods are memory-intractable.
36 pages, 11 figures, 12 tables. Code: this https URL
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computational Engineering, Finance, and Science (cs.CE)
arXiv:2610.04572 [cs.LG]
(or arXiv:2610.04572v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.04572 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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