Convex-skm-net speeds up constraint satisfaction in decision making
Convex-SKM-Net: Low-Latency Block Halfspace Corrections for Neural Convex Constraint Satisfaction
Machine LearningArtificial Intelligence
Summary
Making fast decisions that meet strict rules is important in many areas like robotics and power systems. The authors developed Convex-SKM-Net, a new method that corrects decisions quickly without needing custom steps for each rule. It uses a smart way to handle mistakes and constraints using mathematical tools, running efficiently on GPUs. Their tests show it meets rules accurately and runs much faster than past methods.
What this means in practice
- •For control system engineers: Implement faster constraint corrections in real-time model-predictive control to maintain system safety under strict rules.
- •For power system operators: Use rapid convex relaxation corrections to ensure power grid decisions meet feasibility constraints more efficiently.
Authors
Haoyu Zhu, Xiaochen Zhang, Qingchun Hou
Abstract
Fast inference and strict constraint satisfaction are essential for learning-based decision-making. Existing methods often rely on constraint-specific projections or feasible-set parameterizations, while iterative repair can be costly. We introduce Convex-SKM-Net, a convex constraint-satisfaction layer that forms linearization halfspaces from residual and (sub)gradient oracles without constraint-specific inequality projectors. It applies fixed-depth dual projected-gradient descent (dual PGD) to minimum-displacement block problems using GPU-friendly matrix operations. We jointly learn the predictor and a positive-definite mobility, adapting the correction geometry to improve objective quality. We prove convergence of the outer iterates at fixed dual depth and linear convergence in distance under Slater's condition and bounded subgradients. All our test outputs on three second-order-cone model-predictive control (SOC-MPC) horizons and six power-system convex relaxations satisfy a $10^{-3}$ feasibility tolerance. Comparisons with the latest constraint-satisfaction methods show inference speedups of up to $144.3\times$ on SOC-MPC and $7.7\times$ on a convex quadratically constrained quadratic programming (QCQP) benchmark with joint training. On QCQP, the mean objective gap is $0.012\%$, with full test feasibility at $10^{-4}$. Learning mobility reduces the five-seed affine-task mean gap by $22.4\%$ and improves gaps in matched power-system comparisons.