Are Graph Neural Networks Optimal Approximation Algorithms?
Keywords: graph neural networks, geometric deep learning, discrete optimization, combinatorial optimization, unsupervised learning
TL;DR: Graph Neural Networks are provably optimal approximation algorithms for large class of combinatorial optimization problems, which we also demonstrate empirically.
Abstract: In this work, utilizing powerful algorithmic tools from semidefinite programming (SDP), we design graph neural network architectures that can be used to obtain optimal approximation algorithms for a large class of combinatorial optimization problems.
Concretely, assuming the Unique Games Conjecture, we prove that polynomial-sized message passing algorithms can represent the most powerful polynomial time algorithms for Max Constraint Satisfaction Problems. We leverage this result to construct efficient graph neural network architectures that obtain high-quality approximate solutions on landmark combinatorial optimization problems such as max-cut and maximum independent set. Our approach achieves strong empirical results across a wide range of real-world and synthetic datasets against both neural baselines and classical algorithms. Furthermore, we demonstrate that our method is competitive with standard SDP solvers while enjoying improved scalability and shorter execution times.
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Submission Number: 934
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