Constraint Learning by Optimizing over Trained Neural Networks: A Pragmatic Tutorial
Abstract
Constraint learning is an emerging paradigm of modeling optimization problems with the help of machine learning. In this paradigm, trained machine learning models are embedded into the optimization model. For example, we can learn constraints empirically from available data, or we can avoid using a nonlinear objective function by learning a simpler approximation for it. Neural networks become a compelling option if the machine learning models must capture more elaborate and nuanced relationships. However, optimization models embedding neural networks may become too large or too slow to solve. In this tutorial, we present practical considerations for an effective and efficient use of constraint learning with neural networks and validate it with a case study highlighting the benefit of smaller and sparser networks.
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BibTeX
@misc{fang2026constraint,
title = {{Constraint Learning by Optimizing over Trained Neural Networks: A Pragmatic Tutorial}},
author = {Jiaxiao Fang and Thiago Serra},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35505},
eprint = {2610.35505},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35505},
}
RIS
TY - UNPB
TI - Constraint Learning by Optimizing over Trained Neural Networks: A Pragmatic Tutorial
AU - Jiaxiao Fang
AU - Thiago Serra
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35505
UR - https://arxiv.org/abs/2610.35505
AB - Constraint learning is an emerging paradigm of modeling optimization problems with the help of machine learning. In this paradigm, trained machine learning models are embedded into the optimization model. For example, we can learn constraints empirically from available data, or we can avoid using a nonlinear objective function by learning a simpler approximation for it. Neural networks become a compelling option if the machine learning models must capture more elaborate and nuanced relationships. However, optimization models embedding neural networks may become too large or too slow to solve. In this tutorial, we present practical considerations for an effective and efficient use of constraint learning with neural networks and validate it with a case study highlighting the benefit of smaller and sparser networks.
ER -