Branch-and-bound Our work is Bbased on branch-and-boundBound (BaB), a powerful framework for -2.0 0.5 Lower bound = min(-2.0,

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 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 good 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.

CGF can outperform the GMI cuts for certain distributions.

However, GCP-CROWN currently relies on generic cutting planes ("cuts") generated from external

In this paper,wegeneralize thebound propagation procedure toallowtheaddition of arbitrary cutting plane constraints, including those involving relaxed integer variables that do not appear in existing bound propagation formulations.

Bound propagation methods, when combined with branch and bound, are among the most effective methods to formally verify properties of deep neural networks such as correctness, robustness, and safety. However, existing works cannot handle the general form of cutting plane constraints widely accepted in traditional solvers, which are crucial for strengthening verifiers with tightened convex relaxations. In this paper, we generalize the bound propagation procedure to allow the addition of arbitrary cutting plane constraints, including those involving relaxed integer variables that do not appear in existing bound propagation formulations. Our generalized bound propagation method, GCP-CROWN, opens up the opportunity to apply general cutting plane methods for neural network verification while benefiting from the efficiency and GPU acceleration of bound propagation methods. As a case study, we investigate the use of cutting planes generated by off-the-shelf mixed integer programming (MIP) solver.

However, GCP-CROWN currently relies on generic cutting planes ("cuts") generated from external