Principled Data Augmentation for Learning to Solve Quadratic Programming Problems
This work addresses data scarcity for researchers and practitioners using learning-to-optimize methods in optimization, though it is incremental as it builds on existing MPNN-based approaches.
The paper tackles the challenge of data scarcity in learning-to-optimize methods for quadratic programming problems by introducing a principled data augmentation approach that generates diverse, optimality-preserving instances and integrates them into a self-supervised contrastive learning framework, resulting in improved generalization and effective transfer learning in experiments.
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.