  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.
