Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies
This work addresses the challenge of generalizing branching policies across diverse MILP instances, which is incremental by building on existing imitation learning approaches but with a new parameterization method.
The paper tackled the problem of learning branching policies for Mixed-Integer Linear Programming (MILP) by proposing a novel imitation learning framework that parameterizes the Branch-and-Bound search tree to improve generalization across heterogeneous instances, resulting in policies that significantly outperform the state-of-the-art with higher accuracy and smaller search trees.
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.