Principled Data Augmentation for Learning to Solve Quadratic Programming Problems

TL;DR

This paper proposes a theoretically grounded data augmentation method for message-passing neural networks to improve learning-to-optimize quadratic programming problems, especially in data-scarce scenarios.

Contribution

It introduces a principled data augmentation technique for QPs and integrates it into a self-supervised contrastive learning framework for MPNNs.

Findings

Enhanced generalization in supervised learning-to-optimize tasks.

Improved transfer learning capabilities for related optimization problems.

Robust performance gains in data-scarce environments.

Abstract

Linear and quadratic optimization are crucial in numerous real-world applications, ranging from training machine learning models to solving integer linear programs. Recently, learning-to-optimize methods (L2O) for linear (LPs) or quadratic programs (QPs) using message-passing graph neural networks (MPNNs) have gained traction, promising lightweight, data-driven proxies for solving such optimization problems. For example, they replace the costly computation of strong branching scores in branch-and-bound solvers, thereby reducing the need to solve many such optimization problems. However, robust L2O MPNNs remain challenging in data-scarce settings, especially when addressing complex optimization problems such as QPs. This work introduces a principled approach to data augmentation tailored for QPs via MPNNs. Our method leverages theoretically justified data augmentation techniques to generate diverse yet optimality-preserving instances. Furthermore, we integrate these augmentations into a self-supervised contrastive learning framework, thereby pretraining MPNNs for improved performance on L2O tasks. Extensive experiments demonstrate that our approach improves generalization in supervised scenarios and facilitates effective transfer learning to related optimization problems.