Learning Combinatorial Node Labeling Algorithms

Lukas Gianinazzi, Maximilian Fries, Nikoli Dryden, Tal Ben-Nun, Maciej Besta, Torsten Hoefler

Keywords: graph learning, reinforcement learning, combinatorial optimization

Abstract: We present the combinatorial node labeling framework, which generalizes many prior approaches to solving hard graph optimization problems by supporting problems where solutions consist of arbitrarily many node labels, such as graph coloring. We then introduce a neural network architecture to implement this framework. Our architecture builds on a graph attention network with several inductive biases to improve solution quality and is trained using policy gradient reinforcement learning. We demonstrate our approach on both graph coloring and minimum vertex cover. Our learned heuristics match or outperform classical hand-crafted greedy heuristics and machine learning approaches while taking only seconds on large graphs. We conduct a detailed analysis of the learned heuristics and architecture choices and show that they successfully adapt to different graph structures.

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TL;DR: We present the combinatorial node labeling framework and an accompanying neural network architecture to solve hard graph optimization problems.