arXiv Machine Learning By Jiaxiao Fang, Thiago Serra

Constraint Learning by Optimizing over Trained Neural Networks: A Pragmatic Tutorial

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The article "Constraint Learning by Optimizing over Trained Neural Networks: A Pragmatic Tutorial" discusses the emerging paradigm of embedding trained machine learning models, particularly neural networks, into optimization problems. It explains how constraints can be learned from data or objectives approximated to simplify models, while addressing challenges of size and speed. The tutorial offers practical guidance and demonstrates benefits through a case study that shows smaller, sparser networks can improve efficiency.

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arXiv Machine Learning
Sep 23

CAffNet: Hard Constraint-Affine Neural Networks

arXiv:2605.24437v2 Announce Type: replace Abstract: We present a novel framework for embedding hard constraint satisfaction into neural network (NN) architectures, specifically feedforward neural net...

By Yang Zhao, Jungeun Lee, Jeong hwan Jeon, Sze Zheng Yong
arXiv Machine Learning
Jun 15

Neural Slack Variables for Shape Constraints

arXiv:2606. 13803v1 Announce Type: new Abstract: Enforcing functional inequality constraints such as monotonicity and convexity in neural networks is a fundamental challenge in many industrial and scientific applications.

By Ruben Wiedemann, Antoine Jacquier, Lukas Gonon
arXiv Machine Learning
Sep 16

Learning efficient representations of complex constraints for scalable optimization

The paper introduces PolyFormer, a physics-informed machine learning framework that learns compact polytopic representations of complex constraints. By transforming constraint-induced geometry into efficient polytopic reformulations, PolyFormer reduces optimization complexity and enables the use of standard solvers. Evaluations on large‑scale resource aggregation, network‑constrained optimization, and uncertainty‑aware optimization show up to 6,400‑fold speedups and 99.87% memory savings while keeping feasibility and objective errors low.

By Yilin Wen, Yi Guo, Bo Zhao, Wei Qi, Zechun Hu, Colin Jones, Jian Sun
arXiv AI
Aug 28

CG4AI: A Column Generation Framework for Training AI Models Under Constraints

CG4AI is a column generation framework that trains AI models while enforcing linear constraints on their outputs. It constructs a convex combination of models, using a master linear program to set mixture weights and a pricing subproblem to generate new models guided by dual variables, focusing on the most violated constraints. The method is applied to MNIST digit classification—demonstrating constraint learning, adversarial robustness, error correction, and output relabeling—and to multi‑commodity flow routing, achieving feasible predictors with higher accuracy than single‑model baselines.

By Youcef Magnouche, Abderrahmane Driouch, S\'ebastien Martin, Pierre Bauguion