Revised Note on Learning Algorithms for Quadratic Assignment with Graph Neural Networks

Alex Nowak; Soledad Villar; Afonso S. Bandeira; Joan Bruna

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arXiv · 1706.07450

Revised Note on Learning Algorithms for Quadratic Assignment with Graph Neural Networks

Alex Nowak·Soledad Villar·Afonso S. Bandeira·Joan Bruna

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Abstract

Inverse problems correspond to a certain type of optimization problems formulated over appropriate input distributions. Recently, there has been a growing interest in understanding the computational hardness of these optimization problems, not only in the worst case, but in an average-complexity sense under this same input distribution. In this revised note, we are interested in studying another aspect of hardness, related to the ability to learn how to solve a problem by simply observing a collection of previously solved instances. These 'planted solutions' are used to supervise the training of an appropriate predictive model that parametrizes a broad class of algorithms, with the hope that the resulting model will provide good accuracy-complexity tradeoffs in the average sense. We illustrate this setup on the Quadratic Assignment Problem, a fundamental problem in Network Science. We observe that data-driven models based on Graph Neural Networks offer intriguingly good performance, even in regimes where standard relaxation based techniques appear to suffer.

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Alex Nowak, Soledad Villar, Afonso S. Bandeira, Joan Bruna. 2017-06-22. Revised Note on Learning Algorithms for Quadratic Assignment with Graph Neural Networks. https://arxiv.org/abs/1706.07450

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