  Combinatorial optimization problems are typically tackled by the
branch-and-bound paradigm. We propose a new graph convolutional neural network
model for learning branch-and-bound variable selection policies, which
leverages the natural variable-constraint bipartite graph representation of
mixed-integer linear programs. We train our model via imitation learning from
the strong branching expert rule, and demonstrate on a series of hard problems
that our approach produces policies that improve upon state-of-the-art
machine-learning methods for branching and generalize to instances
significantly larger than seen during training. Moreover, we improve for the
first time over expert-designed branching rules implemented in a
state-of-the-art solver on large problems. Code for reproducing all the
experiments can be found at https://github.com/ds4dm/learn2branch.
