Combinatorial Optimization problems are widespread in domains such as logistics, manufacturing, and drug discovery, yet their NP-hard nature makes them computationally challenging. Recent Neural Combinatorial Optimization (NCO) methods leverage deep learning to learn policies for constructing solutions, trained via Supervised or Reinforcement Learning. While promising, these approaches often rely on task-specific augmentations, perform poorly on out-of-distribution instances, and lack robust inference mechanisms. Moreover, existing latent space models either require labeled data or use an instance-independent latent distribution. In this work, we propose LGS-Net, a novel latent space model that conditions on problem instances, and introduce an efficient inference method, Latent Guided Sampling (LGS), based on Markov Chain Monte Carlo and Stochastic Approximation. We show that the iterations of our method form a time-inhomogeneous Markov Chain and provide rigorous theoretical convergence guarantees. Empirical results on benchmark routing tasks show that our method achieves state-of-the-art performance among NCO baselines.

翻译：摘要：组合优化问题在物流、制造和药物发现等领域广泛存在，但其NP-hard本质导致计算求解极具挑战性。近期神经组合优化方法利用深度学习学习构造解的策略，并通过监督学习或强化学习进行训练。尽管此类方法前景可观，但往往依赖特定任务的数据增强、在分布外实例上表现欠佳，且缺乏鲁棒的推理机制。此外，现有潜在空间模型或需要标注数据，或采用实例无关的潜在分布。本文提出一种新型实例条件化潜在空间模型LGS-Net，并引入基于马尔可夫链蒙特卡洛与随机逼近的高效推理方法——潜在引导采样。我们证明该方法的迭代过程构成非时齐马尔可夫链，并提供了严格的理论收敛性保证。在基准路径规划任务上的实验结果表明，本方法在神经组合优化基线中达到了最先进性能。