  The use of machine learning techniques to improve the performance of
branch-and-bound optimization algorithms is a very active area in the context
of mixed integer linear problems, but little has been done for non-linear
optimization. To bridge this gap, we develop a learning framework for spatial
branching and show its efficacy in the context of the
Reformulation-Linearization Technique for polynomial optimization problems. The
proposed learning is performed offline, based on instance-specific features and
with no computational overhead when solving new instances. Novel graph-based
features are introduced, which turn out to play an important role for the
learning. Experiments on different benchmark instances from the literature show
that the learning-based branching rule significantly outperforms the standard
rules.
