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 imitation learning scheme that mimics the elimination ordering provided by an expert rule. Results show that our imitation learning approach is effective in learning two classical elimination rules: the minimum degree and minimum fill-in heuristics, using simple Graph Neural Network models with only a handful of parameters. Moreover, the learned policies display remarkable generalization performance, across both graphs of larger size, and graphs from a different distribution.

设计用来在数值优化中使用稀疏性的许多技术中，很有影响力的因素是优化问题的图形表示的所谓弦扩展。和弦扩展与使用该扩展的优化算法的性能之间的确定关系不是数学上可以理解的任务。因此，我们遵循当前使用机器学习镜头研究组合优化任务的研究趋势，并设计了一个学习消除规则的框架，以产生高质量的和弦扩展。作为学习框架的第一个构建块，我们提出一种模仿学习方案，该方案模仿专家规则提供的消除顺序。结果表明，我们的模仿学习方法可以有效地学习两个经典消除规则：使用仅带有少量参数的简单Graph Neural Network模型，即可获得最小程度和最小填充启发式算法。此外，所学习的策略在较大尺寸的两个图以及来自不同分布的图上均显示出卓越的泛化性能。