Abstract: Cutting-plane methods have enabled remarkable successes in integer
programming over the last few decades. State-of-the-art solvers integrate a
myriad of cutting-plane techniques to speed up the underlying tree-search
algorithm used to find optimal solutions. In this paper we prove the first
guarantees for learning high-performing cut-selection policies tailored to the
instance distribution at hand using samples. We first bound the sample
complexity of learning cutting planes from the canonical family of
Chv\'atal-Gomory cuts. Our bounds handle any number of waves of any number of
cuts and are fine tuned to the magnitudes of the constraint coefficients. Next,
we prove sample complexity bounds for more sophisticated cut selection policies
that use a combination of scoring rules to choose from a family of cuts.
Finally, beyond the realm of cutting planes for integer programming, we develop
a general abstraction of tree search that captures key components such as node
selection and variable selection. For this abstraction, we bound the sample
complexity of learning a good policy for building the search tree.