A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimization

2024-06-03

International Conference on Machine Learning

AI Summary

In unsupervised neural combinatorial optimization, efficiently sampling from discrete solution spaces remains challenging, as existing methods rely on exact likelihood computation—rendering them incompatible with highly expressive latent-variable models such as diffusion models. Method: This work introduces diffusion models to data-free combinatorial optimization for the first time, proposing a novel training objective based on an upper bound of the reverse KL divergence that eliminates the need for exact likelihood evaluation. We further design discrete-structure-aware embedding representations and a tailored denoising process, enabling direct learning of high-quality solution distributions without supervision. Results: Our approach achieves significant improvements over state-of-the-art methods across multiple benchmark combinatorial optimization tasks, demonstrating superior solution quality, sampling efficiency, and cross-problem generalization—all under a fully unsupervised setting.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Economics, Online Markets and Human Computation: Humans versus LLMs for data annotation and labeling
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based approaches rely primarily on generative models that yield exact sample likelihoods. This work introduces a method that lifts this restriction and opens the possibility to employ highly expressive latent variable models like diffusion models. Our approach is conceptually based on a loss that upper bounds the reverse Kullback-Leibler divergence and evades the requirement of exact sample likelihoods. We experimentally validate our approach in data-free Combinatorial Optimization and demonstrate that our method achieves a new state-of-the-art on a wide range of benchmark problems.

Problem

• Learning to sample from intractable discrete distributions without training data
• Introducing diffusion models for unsupervised combinatorial optimization tasks
• Overcoming the limitation of requiring exact sample likelihoods in generative models

Innovation

• Uses diffusion models for combinatorial optimization
• Employs latent variable models without exact likelihoods
• Bounds reverse KL divergence for unsupervised learning