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

arXiv: https://arxiv.org/abs/2206.13414 · HTML: https://mlsanity.com/paper/2206.13414/

## 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.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Reinforcement Learning for Integer Programming: Learning to Cut](https://mlsanity.com/paper/1906.04859/) (2019)
- [Maximum Resilience of Artificial Neural Networks](https://mlsanity.com/paper/1705.01040/) (2017)
- [Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies](https://mlsanity.com/paper/2002.05120/) (2020)
- [Learning to Select Cuts for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2105.13645/) (2021)
- [Ecole: A Gym-like Library for Machine Learning in Combinatorial Optimization Solvers](https://mlsanity.com/paper/2011.06069/) (2020)
- [Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond](https://mlsanity.com/paper/2106.04033/) (2021)
- [Theoretical challenges towards cutting-plane selection](https://mlsanity.com/paper/1805.02782/) (2018)
- [Cuts, Primal Heuristics, and Learning to Branch for the Time-Dependent Traveling Salesman Problem](https://mlsanity.com/paper/1805.01415/) (2018)

## Built on by (most cited first, 30 of 61)

- [Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model](https://mlsanity.com/paper/2302.00244/) (2023)
- [On Representing Linear Programs by Graph Neural Networks](https://mlsanity.com/paper/2209.12288/) (2022)
- [Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning](https://mlsanity.com/paper/2302.01578/) (2023)
- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programming](https://mlsanity.com/paper/2402.05501/) (2024)
- [On Representing Mixed-Integer Linear Programs by Graph Neural Networks](https://mlsanity.com/paper/2210.10759/) (2022)
- [Machine Learning for Cutting Planes in Integer Programming: A Survey](https://mlsanity.com/paper/2302.09166/) (2023)
- [Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programs](https://mlsanity.com/paper/2406.05938/) (2024)
- [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025)
- [Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methods](https://mlsanity.com/paper/2406.06954/) (2024)
- [Learning to Configure Separators in Branch-and-Cut](https://mlsanity.com/paper/2311.05650/) (2023)
- [Rethinking the Capacity of Graph Neural Networks for Branching Strategy](https://mlsanity.com/paper/2402.07099/) (2024)
- [Learning to Cut via Hierarchical Sequence/Set Model for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2404.12638/) (2024)
- [Are Graph Neural Networks Optimal Approximation Algorithms?](https://mlsanity.com/paper/2310.00526/) (2023)
- [Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Process](https://mlsanity.com/paper/2401.03244/) (2024)
- [Learning To Dive In Branch And Bound](https://mlsanity.com/paper/2301.09943/) (2023)
- [SORREL: Suboptimal-Demonstration-Guided Reinforcement Learning for Learning to Branch](https://mlsanity.com/paper/2412.15534/) (2024)
- [Learning to Stop Cut Generation for Efficient Mixed-Integer Linear Programming](https://mlsanity.com/paper/2401.17527/) (2024)
- [LLMs for Cold-Start Cutting Plane Separator Configuration](https://mlsanity.com/paper/2412.12038/) (2024)
- [EvoCut: Strengthening Integer Programs via Evolution-Guided Language Models](https://mlsanity.com/paper/2508.11850/) (2025)
- [Machine Learning Insides OptVerse AI Solver: Design Principles and Applications](https://mlsanity.com/paper/2401.05960/) (2024)
- [Multi-task Representation Learning for Mixed Integer Linear Programming](https://mlsanity.com/paper/2412.14409/) (2024)
- [Online Learning for Scheduling MIP Heuristics](https://mlsanity.com/paper/2304.03755/) (2023)
- [Metric Learning to Accelerate Convergence of Operator Splitting Methods for Differentiable Parametric Programming](https://mlsanity.com/paper/2404.00882/) (2024)
- [Taking the human out of decomposition-based optimization via artificial intelligence: Part II. Learning to initialize](https://mlsanity.com/paper/2310.07082/) (2023)
- [Learning Backdoors for Mixed Integer Linear Programs with Contrastive Learning](https://mlsanity.com/paper/2401.10467/) (2024)
- [Cutting Plane Selection with Analytic Centers and Multiregression](https://mlsanity.com/paper/2212.07231/) (2022)
- [A Neural Separation Algorithm for the Rounded Capacity Inequalities](https://mlsanity.com/paper/2306.17283/) (2023)
- [Towards graph neural networks for provably solving convex optimization problems](https://mlsanity.com/paper/2502.02446/) (2025)
- [Taking the human out of decomposition-based optimization via artificial intelligence: Part I. Learning when to decompose](https://mlsanity.com/paper/2310.07068/) (2023)

## 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.