Improved Sample Complexity Bounds for Branch-And-Cut

Authors Maria-Florina Balcan, Siddharth Prasad, Tuomas Sandholm, Ellen Vitercik

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Maria-Florina Balcan
  • Computer Science and Machine Learning Departments, Carnegie Mellon University, Pittsburgh, PA, USA
Siddharth Prasad
  • Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA
Tuomas Sandholm
  • Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA
  • Optimized Markets, Inc., Pittsburgh, PA, USA
  • Strategic Machine, Inc., Pittsburgh, PA, USA
  • Strategy Robot, Inc., Pittsburgh, PA, USA
Ellen Vitercik
  • Department of Electrical Engineering and Computer Sciences, University of California Berkeley, CA, USA

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Maria-Florina Balcan, Siddharth Prasad, Tuomas Sandholm, and Ellen Vitercik. Improved Sample Complexity Bounds for Branch-And-Cut. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


The branch-and-cut algorithm for integer programming has a wide variety of tunable parameters that have a huge impact on its performance, but which are challenging to tune by hand. An increasingly popular approach is to use machine learning to configure these parameters based on a training set of integer programs from the application domain. We bound how large the training set should be to ensure that for any configuration, its average performance over the training set is close to its expected future performance. Our guarantees apply to parameters that control the most important aspects of branch-and-cut: node selection, branching constraint selection, and cut selection, and are sharper and more general than those from prior research.

Subject Classification

ACM Subject Classification
  • Theory of computation → Integer programming
  • Theory of computation → Sample complexity and generalization bounds
  • Automated algorithm configuration
  • integer programming
  • machine learning theory
  • tree search
  • branch-and-bound
  • branch-and-cut
  • cutting planes
  • sample complexity
  • generalization guarantees
  • data-driven algorithm design


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