发表机构
LIX (École Polytechnique, IP Paris, CNRS); AMIAD (Agence Ministérielle pour l’IA de Défense)（LIX（巴黎综合理工学院、巴黎综合理工学院联盟、法国国家科学研究中心）; AMIAD（国防人工智能部级机构））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对混合整数线性规划，提出重表述对比学习框架ReMILP，利用等价重表述作为自监督信号，学习变量和约束的通用表示，在多个预测任务中展现有效性与可迁移性。
AI 中文摘要
混合整数线性规划（MILP）为许多现实世界中的决策问题建模，促使机器学习方法利用重复出现的结构来加速MILP求解。MILP可以接受许多等价的重表述：保持整数性的变量变换和添加冗余约束可以改变其表述，同时保持优化问题不变。我们利用这些重表述作为自监督学习的来源，以学习MILP变量和约束的通用表示。我们刻画了对每个输入实例都有效的仿射重表述，并区分了保持变量不变的重新描述和可预测地变换变量的替换。基于等变自监督学习，我们引入了ReMILP（重表述对比MILP表示学习），它联合训练一个图神经网络和一个超网络，以预测变量嵌入在变量变换下如何变换。在没有求解器生成的标签的情况下，ReMILP学习到的表示在未见的问题类别上展现出预期的不变性和等变性。在二元解、约束活动和整数性间隙预测任务中，这些表示在冻结时携带任务相关信息，并为微调提供有用的初始化。
英文摘要
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.
