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 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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2017
- DOI:
- 10.48550/arXiv.1706.07450
- arXiv:
- arXiv:1706.07450
- Bibcode:
- 2017arXiv170607450N
- Keywords:
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- Statistics - Machine Learning;
- Computer Science - Machine Learning
- E-Print:
- Revised note to arXiv:1706.07450v1 that appeared in IEEE Data Science Workshop 2018