arXiv：cs.LG（机器学习，全量分类）· Ousema Bouaneni, Mathis Le Bail, Cl\'ement Elliker, Ma\"el Jenny, Sonia Vanier·· 14 小时前AI 评分34
ReMILP：面向混合整数规划的重新表述对比学习
Reformulation-Contrastive Learning for Mixed Integer Programs
AI 导读
研究者提出 ReMILP，一种利用 MILP 等价重新表述作为自监督信号的表示学习方法，联合训练图神经网络与超网络来预测变量嵌入在变量替换下的变换方式。该方法无需求解器标签，在未见问题类别上展现出预期的不变性与等变性，其冻结表示在二元解、约束活跃度与整数间隙预测任务中均携带任务相关信息，并可作为微调的有效初始化。
正文
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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.00730 [cs.LG] |
| (or arXiv:2610.00730v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.00730 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Mathis Le Bail [view email]
[v1]
Wed, 30 Sep 2026 21:19:40 UTC (1,416 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org