aiqbench analysis
MResOpt introduces a staged residual network architecture that effectively handles constrained optimization by prioritizing constraints through intermediate re-completion and stage-aware losses. Theoretical analysis suggests the model behaves like sequential Gaussian Process regression in the infinite-width limit, while empirical results on power flow benchmarks demonstrate superior high-priority constraint satisfaction compared to reprojected baselines. This approach offers a computationally efficient solution for maintaining iterates on equality manifolds, particularly valuable for domain-specific problems with ordinal structure.
Multi-ResNets for Subspace Preconditioning in Constrained Optimization
arXiv:2606.06300v1 Announce Type: new Abstract: We propose MResOpt, a staged residual neural network architecture for constrained optimization problems. Our architecture fits within predict-complete-correct pipelines and decomposes constraint satisfaction by priority through intermediate re-completion and stage-aware losses. The framework enables domain-informed ordered constraint satisfaction which allows the network to utilize ordinal structure when present. Under an idealized infinite-width regime, we show that our design behaves as sequential Gaussian Process regression. On synthetic QP, QCQP, and SOCP benchmarks, the staged architecture improves high-priority constraint satisfaction across convex and non-convex settings. On line-flow-constrained AC optimal power flow, we introduce a physics-motivated constraint ordering and show that MResOpt supports a learned division of labor that keeps iterates on the equality manifold, achieving substantially lower high-priority violation than reprojected baselines while remaining computationally efficient.
Abstract:We propose MResOpt, a staged residual neural network architecture for constrained optimization problems. Our architecture fits within predict-complete-correct pipelines and decomposes constraint satisfaction by priority through intermediate re-completion and stage-aware losses. The framework enables domain-informed ordered constraint satisfaction which allows the network to utilize ordinal structure when present. Under an idealized infinite-width regime, we show that our design behaves as sequential Gaussian Process regression. On synthetic QP, QCQP, and SOCP benchmarks, the staged architecture improves high-priority constraint satisfaction across convex and non-convex settings. On line-flow-constrained AC optimal power flow, we introduce a physics-motivated constraint ordering and show that MResOpt supports a learned division of labor that keeps iterates on the equality manifold, achieving substantially lower high-priority violation than reprojected baselines while remaining computationally efficient.
Artificial Intelligence (cs.AI)
arXiv:2606.06300 [cs.AI]
(or arXiv:2606.06300v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2606.06300 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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