神经证书定价：组合优化问题的高效求解新方法
评分
55精选理由
方法新颖且理论扎实，实验效果显著，具有较强应用潜力，但限于三类问题，需进一步验证更广泛适用性。
AI 点评
「神经证书定价为组合优化问题提供了一种高效、可泛化的无监督求解范式，有望推动运筹学与深度学习的交叉应用。」
速览
组合优化问题因需指数级搜索而困难，但一旦提供可行解，其结构可行性可多项式验证。本文提出神经证书定价（NCP），利用这种不对称性，通过无监督学习训练神经网络预测证书级对偶价格，结构恢复层构建原始边际解。当证书一致性条件成立时，恢复的边际解全局可行，且一阶误差仅导致目标值二阶损失。在三大类组合优化问题中，NCP显著优于或媲美最先进神经网络基线，计算时间大幅减少，且具有更强的分布外泛化能力。
- 首次提出神经证书定价框架，利用组合优化中搜索与验证的不对称性
- 无监督学习训练，无需标注最优解标签
- 理论证明价格一阶误差仅导致目标值二阶损失
- 在三个组合优化问题集上超越或持平现有方法，计算时间大幅减少
正文
Computer Science > Machine Learning
arXiv:2607.01185v1 (cs) [Submitted on 1 Jul 2026]Title:Neural Certificate Pricing for Combinatorial Optimization Problems
Authors:Jingyi Chen, Xinyuan Zhang, Xinwu Qian View a PDF of the paper titled Neural Certificate Pricing for Combinatorial Optimization Problems, by Jingyi Chen and Xinyuan Zhang and Xinwu Qian View PDF HTML (experimental)Abstract:Combinatorial optimization (CO) problems are difficult because certifiable discrete structure induces exponential search. One needs to search over the set exponentially many candidates to certify optimality, however, the structural feasibility of a path, packing, or cover can be verified in polynomial time once supplied. In this study, we introduce Neural Certificate Pricing (NCP) that exploits this asymmetry under an unsupervised learning framework. A neural network is trained to predict certificate-level dual prices, while a structured recovery layer constructs the induced primal marginal. NCP can be viewed as amortized separation: instead of enumerating violated inequalities, it learns the residual prices through which their aggregate effect enters recovery. When the certificate-consistency condition holds, the recovered marginal is globally feasible, and a local theory shows that first-order errors in the predicted price induce only second-order loss in objective value. Across three classes of CO problems, NCP either outperforms state-of-the-art neural baselines by large margins or matches them at a fraction of the computation time, and shows stronger out-of-distribution generalization.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2607.01185 [cs.LG] |
| (or arXiv:2607.01185v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.01185 Focus to learn more arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Xinwu Qian [view email][v1] Wed, 1 Jul 2026 17:17:55 UTC (466 KB)
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