# Learning to Stop Cut Generation for Efficient Mixed-Integer Linear Programming

arXiv: https://arxiv.org/abs/2401.17527 · HTML: https://mlsanity.com/paper/2401.17527/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 55 references that are in the map.
- First posted on arXiv 31 Jan 2024.

## Builds on (most cited first, 29 of 29)

- [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)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [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)
- [Hybrid Models for Learning to Branch](https://mlsanity.com/paper/2006.15212/) (2020)
- [Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learning](https://mlsanity.com/paper/2206.13414/) (2022)
- [Learning to Select Cuts for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2105.13645/) (2021)
- [Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model](https://mlsanity.com/paper/2302.00244/) (2023)
- [Ecole: A Gym-like Library for Machine Learning in Combinatorial Optimization Solvers](https://mlsanity.com/paper/2011.06069/) (2020)
- [The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insights](https://mlsanity.com/paper/2203.02433/) (2022)
- [Automated Dynamic Algorithm Configuration](https://mlsanity.com/paper/2205.13881/) (2022)
- [Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond](https://mlsanity.com/paper/2106.04033/) (2021)
- [Learning to Compare Nodes in Branch and Bound with Graph Neural Networks](https://mlsanity.com/paper/2210.16934/) (2022)
- [Lookback for Learning to Branch](https://mlsanity.com/paper/2206.14987/) (2022)
- [Adaptive Cut Selection in Mixed-Integer Linear Programming](https://mlsanity.com/paper/2202.10962/) (2022)
- [Sample-Efficient Reinforcement Learning via Conservative Model-Based Actor-Critic](https://mlsanity.com/paper/2112.10504/) (2021)
- [Learning Robust Policy against Disturbance in Transition Dynamics via State-Conservative Policy Optimization](https://mlsanity.com/paper/2112.10513/) (2021)
- [Learning Task-relevant Representations for Generalization via Characteristic Functions of Reward Sequence Distributions](https://mlsanity.com/paper/2205.10218/) (2022)
- [Robust Representation Learning by Clustering with Bisimulation Metrics for Visual Reinforcement Learning with Distractions](https://mlsanity.com/paper/2302.12003/) (2023)
- [Deep Model-Based Reinforcement Learning via Estimated Uncertainty and Conservative Policy Optimization](https://mlsanity.com/paper/1911.12574/) (2019)
- [Learning to Use Local Cuts](https://mlsanity.com/paper/2206.11618/) (2022)
- [Efficient Exploration in Resource-Restricted Reinforcement Learning](https://mlsanity.com/paper/2212.06988/) (2022)

## Built on by (most cited first, 8 of 8)

- [Energy-Guided Diffusion Sampling for Offline-to-Online Reinforcement Learning](https://mlsanity.com/paper/2407.12448/) (2024)
- [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025)
- [CA-I2P: Channel-Adaptive Registration Network with Global Optimal Selection](https://mlsanity.com/paper/2506.21364/) (2025)
- [Accurate and Scalable Graph Neural Networks via Message Invariance](https://mlsanity.com/paper/2502.19693/) (2025)
- [How hard is learning to cut? Trade-offs and sample complexity](https://mlsanity.com/paper/2506.00252/) (2025)
- [A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attention](https://mlsanity.com/paper/2601.04509/) (2026)
- [FourierCSP: Differentiable Constraint Satisfaction Problem Solving by Walsh-Fourier Expansion](https://mlsanity.com/paper/2510.04480/) (2025)
- [SRG: Score-based Relaxation-guided Generation for Mixed Integer Linear Programming](https://mlsanity.com/paper/2603.24033/) (2026)

## Abstract (arXiv)

Cutting planes (cuts) play an important role in solving mixed-integer linear programs (MILPs), as they significantly tighten the dual bounds and improve the solving performance. A key problem for cuts is when to stop cuts generation, which is important for the efficiency of solving MILPs. However, many modern MILP solvers employ hard-coded heuristics to tackle this problem, which tends to neglect underlying patterns among MILPs from certain applications. To address this challenge, we formulate the cuts generation stopping problem as a reinforcement learning problem and propose a novel hybrid graph representation model (HYGRO) to learn effective stopping strategies. An appealing feature of HYGRO is that it can effectively capture both the dynamic and static features of MILPs, enabling dynamic decision-making for the stopping strategies. To the best of our knowledge, HYGRO is the first data-driven method to tackle the cuts generation stopping problem. By integrating our approach with modern solvers, experiments demonstrate that HYGRO significantly improves the efficiency of solving MILPs compared to competitive baselines, achieving up to 31% improvement.