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About this paper
Max B. Paulus, Giulia Zarpellon, Andreas Krause, Laurent Charlin, Chris J. Maddison
This research from ETH Zürich, Vector Institute, HEC Montréal, and University of Toronto introduces NeuralCut, an imitation learning framework that trains a graph neural network to select cutting planes in Mixed-Integer Linear Programming (MILP) by learning from a computationally intensive "lookahead" expert. The method effectively closes the integrality gap on synthetic benchmarks and, when integrated into a full Branch-and-Cut solver, reduces MILP solving time by up to 10% on neural network verification instances while using fewer cuts.
Key insights
- Explicitly measuring the dual bound improvement (lookahead) for candidate cuts provides a superior oracle for cut selection compared to traditional heuristics.
- Imitation learning can effectively transfer the knowledge from this computationally expensive but high-quality oracle into an efficient, deployable machine learning model.
- A specialized graph neural network architecture, capable of processing the intricate relationships within MILP states, is crucial for learning effective and transferable cut selection policies.
Summary by alphaXiv.
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