Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learning
This work addresses cut selection for MILP solvers, offering a learning-based improvement over manual heuristics, but it is incremental as it builds on existing imitation learning methods.
The paper tackles the problem of selecting cutting planes in mixed-integer linear programming by proposing a neural architecture (NeuralCut) that uses imitation learning to mimic an expensive lookahead expert, resulting in outperformance over standard baselines on synthetic benchmarks and validation in a neural network verification solver.
Cutting planes are essential for solving mixed-integer linear problems (MILPs), because they facilitate bound improvements on the optimal solution value. For selecting cuts, modern solvers rely on manually designed heuristics that are tuned to gauge the potential effectiveness of cuts. We show that a greedy selection rule explicitly looking ahead to select cuts that yield the best bound improvement delivers strong decisions for cut selection - but is too expensive to be deployed in practice. In response, we propose a new neural architecture (NeuralCut) for imitation learning on the lookahead expert. Our model outperforms standard baselines for cut selection on several synthetic MILP benchmarks. Experiments with a B&C solver for neural network verification further validate our approach, and exhibit the potential of learning methods in this setting.