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This research introduces ReMILP, a self-supervised learning framework that uses affine reformulations of mixed-integer linear programs to train graph neural networks without relying on solver-derived labels. By leveraging equivariant properties inherent to mathematical optimization structures, the method learns robust variable embeddings that improve prediction tasks and accelerate solving for unseen problem classes. The work represents a significant advancement in applying machine learning techniques directly to the structural symmetries of classical optimization problems.
Reformulation-Contrastive Learning for Mixed Integer Programs
arXiv:2610.00730v1 Announce Type: new Abstract: Mixed-integer linear programs (MILP) model many real-world decision problems, motivating machine-learning methods that exploit recurring structure to accelerate MILP solving. MILPs can admit many equivalent formulations: integrality-preserving changes of variables and the addition of redundant constraints can alter their formulations while preserving the optimization problem. We leverage these reformulations as a source of self-supervision for learning general-purpose representations of MILP variables and constraints. We characterize the affine reformulations that are valid for every input instance, and distinguish re-descriptions, which leave variables unchanged, from substitutions, which transform them predictably. Building on equivariant self-supervised learning, we introduce ReMILP (reformulation-contrastive MILP representation learning), which jointly trains a graph neural network and a hypernetwork to predict how variable embeddings transform under changes of variables. Without solver-derived labels, ReMILP learns representations that exhibit the intended invariance and equivariance on unseen problem classes. Across binary solution, constraint activity and integrality gap prediction, these representations carry task-relevant information when frozen and provide a useful initialization for fine-tuning.
Abstract:Mixed-integer linear programs (MILP) model many real-world decision problems, motivating machine-learning methods that exploit recurring structure to accelerate MILP solving. MILPs can admit many equivalent formulations: integrality-preserving changes of variables and the addition of redundant constraints can alter their formulations while preserving the optimization problem. We leverage these reformulations as a source of self-supervision for learning general-purpose representations of MILP variables and constraints. We characterize the affine reformulations that are valid for every input instance, and distinguish re-descriptions, which leave variables unchanged, from substitutions, which transform them predictably. Building on equivariant self-supervised learning, we introduce ReMILP (reformulation-contrastive MILP representation learning), which jointly trains a graph neural network and a hypernetwork to predict how variable embeddings transform under changes of variables. Without solver-derived labels, ReMILP learns representations that exhibit the intended invariance and equivariance on unseen problem classes. Across binary solution, constraint activity and integrality gap prediction, these representations carry task-relevant information when frozen and provide a useful initialization for fine-tuning.
Machine Learning (cs.LG)
arXiv:2610.00730 [cs.LG]
(or arXiv:2610.00730v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.00730 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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