让机器学习约束满足真实可行性，概率保障不越界
Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees
- 用置信预测方法确保学习的约束不会违反真实限制
- 在真实场景中达成目标可行性率，计算成本更低
- 适合需严格约束保证的工业优化决策场景
我们提出一种新型框架C-MICL，为数据驱动的优化约束提供概率可行性保障。标准混合整数约束学习方法常因模型误差或数据不足而违反真实约束，而C-MICL利用置信预测，在条件独立假设下，以至少1−α的概率确保解是真可行的。该框架无需访问真实约束函数，同时支持回归与分类任务，且避免了基于集成的启发式方法带来的可扩展性问题。在真实应用中的实验表明，C-MICL能稳定实现目标可行性率，保持良好目标性能，并显著降低计算开销。本工作连接数学优化与机器学习，为决策系统中引入带有不确定性感知的约束提供了严谨的统计保障。
原文摘要 · Abstract (English)
We propose Conformal Mixed-Integer Constraint Learning (C-MICL), a novel framework that provides probabilistic feasibility guarantees for data-driven constraints in optimization problems. While standard Mixed-Integer Constraint Learning methods often violate the true constraints due to model error or data limitations, our C-MICL approach leverages conformal prediction to ensure feasible solutions are ground-truth feasible. This guarantee holds with probability at least $1{-}α$, under a conditional independence assumption. The proposed framework supports both regression and classification tasks without requiring access to the true constraint function, while avoiding the scalability issues associated with ensemble-based heuristics. Experiments on real-world applications demonstrate that C-MICL consistently achieves target feasibility rates, maintains competitive objective performance, and significantly reduces computational cost compared to existing methods. Our work bridges mathematical optimization and machine learning, offering a principled approach to incorporate uncertainty-aware constraints into decision-making with rigorous statistical guarantees.
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