  Branch and Bound (B&B) is the exact tree search method typically used to
solve Mixed-Integer Linear Programming problems (MILPs). Learning branching
policies for MILP has become an active research area, with most works proposing
to imitate the strong branching rule and specialize it to distinct classes of
problems. We aim instead at learning a policy that generalizes across
heterogeneous MILPs: our main hypothesis is that parameterizing the state of
the B&B search tree can aid this type of generalization. We propose a novel
imitation learning framework, and introduce new input features and
architectures to represent branching. Experiments on MILP benchmark instances
clearly show the advantages of incorporating an explicit parameterization of
the state of the search tree to modulate the branching decisions, in terms of
both higher accuracy and smaller B&B trees. The resulting policies
significantly outperform the current state-of-the-art method for "learning to
branch" by effectively allowing generalization to generic unseen instances.
