  Over the last few years, there has been a surge in the use of learning
techniques to improve the performance of optimization algorithms. In
particular, the learning of branching rules in mixed integer linear programming
has received a lot of attention, with most methodologies based on strong
branching imitation. Recently, some advances have been made as well in the
context of nonlinear programming, with some methodologies focusing on learning
to select the best branching rule among a predefined set of rules leading to
promising results. In this paper we explore, in the nonlinear setting, the
limits on the improvements that might be achieved by the above two approaches:
learning to select the best variable (strong branching) and learning to select
the best rule (rule selection).
