Papers › Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphs

Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphs

18 Jun 2020NeurIPS 2020 12arXiv:2006.10643archive 2025-07-28

Nikolaos Karalias, Andreas Loukas

Combinatorial optimization problems are notoriously challenging for neural networks, especially in the absence of labeled instances. This work proposes an unsupervised learning framework for CO problems on graphs that can provide integral solutions of certified quality. Inspired by Erdos' probabilistic method, we use a neural network to parametrize a probability distribution over sets. Crucially, we show that when the network is optimized w.r.t. a suitably chosen loss, the learned distribution contains, with controlled probability, a low-cost integral solution that obeys the constraints of the combinatorial problem. The probabilistic proof of existence is then derandomized to decode the desired solutions. We demonstrate the efficacy of this approach to obtain valid solutions to the maximum clique problem and to perform local graph clustering. Our method achieves competitive results on both real datasets and synthetic hard instances.

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Stalence/erdos_neu officialmentioned in paperpytorch report
shengyu-feng/rld4co mentioned on GitHubpytorch report

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ClusteringCombinatorial OptimizationGraph Clustering

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