# Learning chordal extensions

arXiv: https://arxiv.org/abs/1910.07600 · HTML: https://mlsanity.com/paper/1910.07600/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- First posted on arXiv 16 Oct 2019.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Built on by (most cited first, 5 of 5)

- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [LeNSE: Learning To Navigate Subgraph Embeddings for Large-Scale Combinatorial Optimisation](https://mlsanity.com/paper/2205.10106/) (2022)
- [A machine learning framework for neighbor generation in metaheuristic search](https://mlsanity.com/paper/2212.11451/) (2022)
- [Revisiting local branching with a machine learning lens](https://mlsanity.com/paper/2112.02195/) (2021)
- [Deep RL Dual Sourcing Inventory Management with Supply and Capacity Risk Awareness](https://mlsanity.com/paper/2507.14446/) (2025)

## Abstract (arXiv)

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.