  We propose a Reinforcement Learning based approach to approximately solve the
Tree Decomposition (TD) problem. TD is a combinatorial problem, which is
central 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 combinatorial
problems can be successively solved by learned heuristics. However, the
majority of existing works do not address the question of the generalization of
learning-based solutions. Our model is based on the graph convolution neural
network (GCN) for learning graph representations. We show that the agent
builton GCN and trained on a single graph using an Actor-Critic method can
efficiently generalize to real-world TD problem instances. We establish that
our method successfully generalizes from small graphs, where TD can be found by
exact algorithms, to large instances of practical interest, while still having
very low time-to-solution. On the other hand, the agent-based approach
surpasses all greedy heuristics by the quality of the solution.
