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[2602.13155] Learning to Approximate Uniform Facility Location via Graph Neural Networks
Summary
This paper explores a novel approach using Graph Neural Networks (GNNs) to solve the Uniform Facility Location problem, merging learning-based methods with classical approximation algorithms.
Why It Matters
The research addresses the limitations of existing learning-based optimization techniques by providing a differentiable model that maintains performance guarantees, potentially transforming applications in logistics and data clustering. This work bridges the gap between traditional algorithms and modern machine learning approaches, enhancing efficiency in solving complex combinatorial problems.
Key Takeaways
- Introduces a differentiable MPNN model for Uniform Facility Location.
- Avoids reliance on supervised training and discrete relaxations.
- Demonstrates superior performance compared to traditional approximation algorithms.
- Provides provable approximation and scalability guarantees.
- Bridges the gap between learning-based methods and classical optimization.
Computer Science > Machine Learning arXiv:2602.13155 (cs) [Submitted on 13 Feb 2026] Title:Learning to Approximate Uniform Facility Location via Graph Neural Networks Authors:Chendi Qian, Christopher Morris, Stefanie Jegelka, Christian Sohler View a PDF of the paper titled Learning to Approximate Uniform Facility Location via Graph Neural Networks, by Chendi Qian and 3 other authors View PDF HTML (experimental) Abstract:There has been a growing interest in using neural networks, especially message-passing neural networks (MPNNs), to solve hard combinatorial optimization problems heuristically. However, existing learning-based approaches for hard combinatorial optimization tasks often rely on supervised training data, reinforcement learning, or gradient estimators, leading to significant computational overhead, unstable training, or a lack of provable performance guarantees. In contrast, classical approximation algorithms offer such performance guarantees under worst-case inputs but are non-differentiable and unable to adaptively exploit structural regularities in natural input distributions. We address this dichotomy with the fundamental example of Uniform Facility Location (UniFL), a variant of the combinatorial facility location problem with applications in clustering, data summarization, logistics, and supply chain design. We develop a fully differentiable MPNN model that embeds approximation-algorithmic principles while avoiding the need for solver supervision or discr...