Latent Guided Sampling for Combinatorial Optimization

TL;DR

This paper introduces LGS-Net, a latent space model with an efficient sampling method for combinatorial optimization, achieving state-of-the-art results in routing tasks with theoretical convergence guarantees.

Contribution

The work presents a novel latent space model and a sampling method that improves solution quality and robustness in combinatorial optimization, with theoretical and empirical validation.

Findings

Achieves state-of-the-art performance on routing benchmarks.

Provides rigorous convergence guarantees for the sampling method.

Outperforms existing RL-based approaches in out-of-distribution instances.

Abstract

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 methods leverage deep learning to learn solution strategies, trained via Supervised or Reinforcement Learning (RL). 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 rely on pre-trained policies. 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 RL-based approaches.