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arXiv · 1910.07600

Learning chordal extensions

Defeng Liu·Andrea Lodi·Mathieu Tanneau
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Abstract

A highly influential ingredient of many techniques designed to exploit sparsity in numerical optimization is the so-called chordal extension of a graph representation of the optimization problem. The definitive relation between chordal extension and the performance of the optimization algorithm that uses the extension is not a mathematically understood task. For this reason, we follow the current research trend of looking at Combinatorial Optimization tasks by using a Machine Learning lens, and we devise a framework for learning elimination rules yielding high-quality chordal extensions. As a first building block of the learning framework, we propose an on-policy imitation learning scheme that mimics the elimination ordering provided by the (classical) minimum degree rule. The results show that our on-policy imitation learning approach is effective in learning the minimum degree policy and, consequently, produces graphs with desirable fill-in characteristics.

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Defeng Liu, Andrea Lodi, Mathieu Tanneau. 2019-10-16. Learning chordal extensions. https://arxiv.org/abs/1910.07600

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