mlsanityData to 14 Oct 2026

Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learning

arXiv 2206.13414 ↗First posted 27 Jun 2022cs.LG math.OC stat.MLcited by 61

On the map: Offline RL and imitation learning from data → Imitation learning methods

Abstract (arXiv)

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.

Key facts. Cited by 61 papers in the map (data through 14 Oct 2026). Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data. Builds on 17 of its 37 references that are in the map. First posted on arXiv 27 Jun 2022.

Builds on

17 of 37 references.

References · 17

  1. 2017Attention Is All You Needcited by 60,361
  2. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  4. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 7,005
  5. 2020Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classificationcited by 506
  6. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 328
  7. 2019Exact Combinatorial Optimization with Graph Convolutional Neural Networkscited by 318
  8. 2021Combinatorial optimization and reasoning with graph neural networkscited by 268
  9. 2020Solving Mixed Integer Programs Using Neural Networkscited by 182
  10. 2019Reinforcement Learning for Integer Programming: Learning to Cutcited by 111
  11. 2017Maximum Resilience of Artificial Neural Networkscited by 97
  12. 2020Parameterizing Branch-and-Bound Search Trees to Learn Branching Policiescited by 63
5 more
  1. 2021Learning to Select Cuts for Efficient Mixed-Integer Programmingcited by 48
  2. 2020Ecole: A Gym-like Library for Machine Learning in Combinatorial Optimization Solverscited by 43
  3. 2021Sample Complexity of Tree Search Configuration: Cutting Planes and Beyondcited by 33
  4. 2018Theoretical challenges towards cutting-plane selectioncited by 16
  5. 2018Cuts, Primal Heuristics, and Learning to Branch for the Time-Dependent Traveling Salesman Problemcited by 11

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 3; 2023: 11; 2024: 20; 2025: 14; 2026: 13.

61 papers.

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  1. 2023Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Modelcited by 45
  2. 2022On Representing Linear Programs by Graph Neural Networkscited by 39
  3. 2023Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learningcited by 37
  4. 2024Towards Foundation Models for Mixed Integer Linear Programmingcited by 31
  5. 2024Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programmingcited by 24
  6. 2022On Representing Mixed-Integer Linear Programs by Graph Neural Networkscited by 23
  7. 2023Machine Learning for Cutting Planes in Integer Programming: A Surveycited by 20
  8. 2024Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programscited by 16
  9. 2025Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programmingcited by 16
  10. 2024Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methodscited by 15
  11. 2023Learning to Configure Separators in Branch-and-Cutcited by 14
  12. 2024Rethinking the Capacity of Graph Neural Networks for Branching Strategycited by 12
38 more
  1. 2024Learning to Cut via Hierarchical Sequence/Set Model for Efficient Mixed-Integer Programmingcited by 12
  2. 2023Are Graph Neural Networks Optimal Approximation Algorithms?cited by 11
  3. 2024Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Processcited by 11
  4. 2023Learning To Dive In Branch And Boundcited by 10
  5. 2024SORREL: Suboptimal-Demonstration-Guided Reinforcement Learning for Learning to Branchcited by 9
  6. 2024Learning to Stop Cut Generation for Efficient Mixed-Integer Linear Programmingcited by 8
  7. 2024LLMs for Cold-Start Cutting Plane Separator Configurationcited by 8
  8. 2025EvoCut: Strengthening Integer Programs via Evolution-Guided Language Modelscited by 8
  9. 2024Machine Learning Insides OptVerse AI Solver: Design Principles and Applicationscited by 7
  10. 2024Multi-task Representation Learning for Mixed Integer Linear Programmingcited by 7
  11. 2023Online Learning for Scheduling MIP Heuristicscited by 6
  12. 2024Metric Learning to Accelerate Convergence of Operator Splitting Methods for Differentiable Parametric Programmingcited by 6
  13. 2023Taking the human out of decomposition-based optimization via artificial intelligence: Part II. Learning to initializecited by 5
  14. 2024Learning Backdoors for Mixed Integer Linear Programs with Contrastive Learningcited by 5
  15. 2022Cutting Plane Selection with Analytic Centers and Multiregressioncited by 4
  16. 2023A Neural Separation Algorithm for the Rounded Capacity Inequalitiescited by 4
  17. 2025Towards graph neural networks for provably solving convex optimization problemscited by 4
  18. 2023Taking the human out of decomposition-based optimization via artificial intelligence: Part I. Learning when to decomposecited by 3
  19. 2023Differentiable Cutting-plane Layers for Mixed-integer Linear Optimizationcited by 3
  20. 2025When GNNs meet symmetry in ILPs: an orbit-based feature augmentation approachcited by 3
  21. 2025Beyond Local Selection: Global Cut Selection for Enhanced Mixed-Integer Programmingcited by 2
  22. 2025FORGE: Foundational Optimization Representations from Graph Embeddingscited by 2
  23. 2025Planning in Branch-and-Bound: Model-Based Reinforcement Learning for Exact Combinatorial Optimizationcited by 2
  24. 2025Graph-Based Imitation and Reinforcement Learning for Efficient Benders Decompositioncited by 2
  25. 2024Deep learning enhanced mixed integer optimization: Learning to reduce model dimensionalitycited by 1
  26. 2024Learning optimal objective values for MILPcited by 1
  27. 2024RL-SPH: Learning to Achieve Feasible Solutions for Integer Linear Programscited by 1
  28. 2025How hard is learning to cut? Trade-offs and sample complexitycited by 1
  29. 2025Solve Smart, Not Often: Policy Learning for Costly MILP Re-solvingcited by 1
  30. 2026A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attentioncited by 1
  31. 2026Solving Max-Cut to Global Optimality via Feasibility-Preserving Graph Neural Networkscited by 1
  32. 2026MILP-Evo: Closed-Loop Fully Automatic Design of MILP Solverscited by 1
  33. 2024Supplementary Materials to Graph Convolutional Branch and Boundcited by 0
  34. 2024Learn2Aggregate: Supervised Generation of Chv'atal-Gomory Cuts Using Graph Neural Networkscited by 0
  35. 2024Towards An Unsupervised Learning Scheme for Efficiently Solving Parameterized Mixed-Integer Programscited by 0
  36. 2025Generalization Guarantees for Learning Branch-and-Cut Policies in Integer Programmingcited by 0
  37. 2025Collab-Solver: Collaborative Solving Policy Learning for Mixed-Integer Linear Programmingcited by 0
  38. 2025Feature Augmentation of GNNs for ILPs: Local Uniqueness Sufficescited by 0

50 most cited of 61 All 61 (JSON)

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  1. 2021Learning a Large Neighborhood Search Algorithm for Mixed Integer Programs
  2. 2026Feasibility-Aware Imitation Learning for Benders Decomposition
  3. 2026Learning to Cut: Reinforcement Learning for Benders Decomposition
  4. 2022Learning to Accelerate Approximate Methods for Solving Integer Programming via Early Fixing
  5. 2025ASAP: Exploiting the Satisficing Generalization Edge in Neural Combinatorial Optimization
  6. 2025A Dataless Reinforcement Learning Approach to Rounding Hyperplane Optimization for Max-Cut
  7. 2025Improvement of Optimization using Learning Based Models in Mixed Integer Linear Programming Tasks
  8. 2022Branch Ranking for Efficient Mixed-Integer Programming via Offline Ranking-based Policy Learning