Latent Guided Sampling for Combinatorial Optimization

2025-06-04

AI Summary

Neural combinatorial optimization methods suffer from poor generalization, weak out-of-distribution (OOD) performance, and brittle inference when tackling NP-hard problems. Method: We propose a label-free, pretraining-free framework for latent-space modeling and inference. Our approach introduces instance-conditioned latent-space modeling and a novel Latent Guided Sampling (LGS) mechanism, integrating MCMC, stochastic approximation, and conditional encoding. Contribution/Results: Theoretically, we establish for the first time that LGS iterations form a non-homogeneous Markov chain and provide rigorous convergence guarantees. Empirically, on standard path-planning benchmarks, our method matches or exceeds the best reinforcement learning–based approaches, while significantly improving OOD generalization and solution stability—without requiring ground-truth labels or pretrained models.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Solving NP-hard combinatorial optimization challenges efficiently
• Improving neural methods for out-of-distribution generalization
• Developing label-free latent space models for optimization

Innovation

• Latent space model conditioning on problem instances
• Efficient inference via Markov Chain Monte Carlo
• Stochastic Approximation for robust convergence