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We propose a Reinforcement Learning based approach to approximately solve theTree Decomposition (TD) problem. TD is a combinatorial problem, which iscentral to the analysis of graph minor structure and computational complexity,as well as in the algorithms of probabilistic inference, register allocation,and other practical tasks. Recently, it has been shown that combinatorialproblems can be successively solved by learned heuristics. However, themajority of existing works do not address the question of the generalization oflearning-based solutions. Our model is based on the graph convolution neuralnetwork (GCN) for learning graph representations. We show that the agentbuilton GCN and trained on a single graph using an Actor-Critic method canefficiently generalize to real-world TD problem instances. We establish thatour method successfully generalizes from small graphs, where TD can be found byexact algorithms, to large instances of practical interest, while still havingvery low time-to-solution. On the other hand, the agent-based approachsurpasses all greedy heuristics by the quality of the solution.

Graph Convolutional Policy for Solving Tree Decomposition via Reinforcement Learning Heuristics