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An Extended Validity Domain for Constraint Learning
Preprint   Open access

An Extended Validity Domain for Constraint Learning

Yilin Zhu and Samuel Burer
arXiv.org
Cornell University
06/14/2024
DOI: 10.48550/arxiv.2406.10065
url
https://doi.org/10.48550/arxiv.2406.10065View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We consider embedding a predictive machine-learning model within a prescriptive optimization problem. In this setting, called constraint learning, we study the concept of a validity domain, i.e., a constraint added to the feasible set, which keeps the optimization close to the training data, thus helping to ensure that the computed optimal solution exhibits less prediction error. In particular, we propose a new validity domain which uses a standard convex-hull idea but in an extended space. We investigate its properties and compare it empirically with existing validity domains on a set of test problems for which the ground truth is known. Results show that our extended convex hull routinely outperforms existing validity domains, especially in terms of the function value error, that is, it exhibits closer agreement between the true function value and the predicted function value at the computed optimal solution. We also consider our approach within two stylized optimization models, which show that our method reduces feasibility error, as well as a real-world pricing case study.
Mathematics - Optimization and Control

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