Revised Note on Learning Algorithms for Quadratic Assignment with Graph Neural Networks
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 averagecomplexity 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 accuracycomplexity tradeoffs in the average sense. We illustrate this setup on the Quadratic Assignment Problem, a fundamental problem in Network Science. We observe that datadriven models based on Graph Neural Networks offer intriguingly good performance, even in regimes where standard relaxation based techniques appear to suffer.
 Publication:

arXiv eprints
 Pub Date:
 June 2017
 arXiv:
 arXiv:1706.07450
 Bibcode:
 2017arXiv170607450N
 Keywords:

 Statistics  Machine Learning;
 Computer Science  Machine Learning
 EPrint:
 Revised note to arXiv:1706.07450v1 that appeared in IEEE Data Science Workshop 2018