  The branch-and-cut algorithm is the method of choice to solve large scale
integer programming problems in practice. A key ingredient of branch-and-cut is
the use of cutting planes which are derived constraints that reduce the search
space for an optimal solution. Selecting effective cutting planes to produce
small branch-and-cut trees is a critical challenge in the branch-and-cut
algorithm. Recent advances have employed a data-driven approach to select
optimal cutting planes from a parameterized family, aimed at reducing the
branch-and-bound tree size (in expectation) for a given distribution of integer
programming instances. We extend this idea to the selection of the best cut
generating function (CGF), which is a tool in the integer programming
literature for generating a wide variety of cutting planes that generalize the
well-known Gomory Mixed-Integer (GMI) cutting planes. We provide rigorous
sample complexity bounds for the selection of an effective CGF from certain
parameterized families that provably performs well for any specified
distribution on the problem instances. Our empirical results show that the
selected CGF can outperform the GMI cuts for certain distributions.
Additionally, we explore the sample complexity of using neural networks for
instance-dependent CGF selection.
