Learning chordal extensions

TL;DR

This paper introduces a machine learning framework to learn elimination rules for chordal extensions in graphs, aiming to improve optimization performance by producing better fill-in characteristics.

Contribution

It proposes an on-policy imitation learning method to replicate the minimum degree rule for chordal extension, enhancing graph fill-in quality.

Findings

Effective learning of minimum degree policy

Graphs with improved fill-in characteristics

Potential for better optimization performance

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.