Learning chordal extensions
This work addresses a combinatorial optimization bottleneck in sparse numerical methods, offering an incremental improvement by applying machine learning to an existing heuristic.
The paper tackles the problem of finding high-quality chordal extensions for sparse numerical optimization by developing a machine learning framework that learns elimination rules, specifically using on-policy imitation learning to mimic the classical minimum degree rule. The results show this approach effectively learns the policy and produces graphs with desirable fill-in characteristics.
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.