  Cutting-planes are one of the most important building blocks for solving
large-scale integer programming (IP) problems to (near) optimality. The
majority of cutting plane approaches rely on explicit rules to derive valid
inequalities that can separate the target point from the feasible set. Local
cuts, on the other hand, seek to directly derive the facets of the underlying
polyhedron and use them as cutting planes. However, current approaches rely on
solving Linear Programming (LP) problems in order to derive such a hyperplane.
In this paper, we present a novel generic approach for learning the facets of
the underlying polyhedron by accessing it implicitly via an enumeration oracle
in a reduced dimension. This is achieved by embedding the oracle in a variant
of the Frank-Wolfe algorithm which is capable of generating strong cutting
planes, effectively turning the enumeration oracle into a separation oracle. We
demonstrate the effectiveness of our approach with a case study targeting the
multidimensional knapsack problem (MKP).
