Learning to Approximate Uniform Facility Location via Graph Neural Networks

TL;DR

This paper introduces a differentiable graph neural network for Uniform Facility Location that combines classical approximation guarantees with empirical improvements, avoiding supervision or relaxations.

Contribution

It presents a novel fully differentiable MPNN model that integrates approximation principles, providing theoretical guarantees and practical performance gains.

Findings

Model has provable approximation guarantees.

Empirically outperforms standard approximation algorithms.

Narrowing the gap to integer linear programming solutions.

Abstract

Neural networks, particularly message-passing neural networks (MPNNs), are increasingly used as heuristics for hard combinatorial optimization problems. Yet many learning-based methods rely on supervision, reinforcement learning, or gradient estimators, causing high computational cost, unstable training, or limited guarantees. Classical approximation algorithms provide worst-case guarantees but are non-differentiable and cannot adapt to structure in natural input distributions. We study this tradeoff through Uniform Facility Location (UniFL), a problem with applications in clustering, summarization, logistics, and supply chains. We propose a fully differentiable MPNN that incorporates approximation-algorithmic principles without solver supervision or discrete relaxations. The model has provable approximation guarantees and empirically improves on standard approximation algorithms, narrowing the gap to integer linear programming.