Title: Learning Combinatorial Node Labeling Algorithms. 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.