# CAMBranch: Contrastive Learning with Augmented MILPs for Branching

arXiv: https://arxiv.org/abs/2402.03647 · HTML: https://mlsanity.com/paper/2402.03647/

## Key facts

- Cited by 10 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 30 of its 54 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Placed in

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

## Builds on (most cited first, 30 of 30)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [DeCLUTR: Deep Contrastive Learning for Unsupervised Textual Representations](https://mlsanity.com/paper/2006.03659/) (2020)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Are Graph Augmentations Necessary? Simple Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2112.08679/) (2021)
- [CERT: Contrastive Self-supervised Learning for Language Understanding](https://mlsanity.com/paper/2005.12766/) (2020)
- [Hybrid Models for Learning to Branch](https://mlsanity.com/paper/2006.15212/) (2020)
- [Learning to Branch](https://mlsanity.com/paper/1803.10150/) (2018)
- [Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies](https://mlsanity.com/paper/2002.05120/) (2020)
- [A Framework For Contrastive Self-Supervised Learning And Designing A New Approach](https://mlsanity.com/paper/2009.00104/) (2020)
- [Pretraining with Contrastive Sentence Objectives Improves Discourse Performance of Language Models](https://mlsanity.com/paper/2005.10389/) (2020)
- [Learning to branch with Tree MDPs](https://mlsanity.com/paper/2205.11107/) (2022)
- [A Survey for Solving Mixed Integer Programming via Machine Learning](https://mlsanity.com/paper/2203.02878/) (2022)
- [A Theoretical and Computational Analysis of Full Strong-Branching](https://mlsanity.com/paper/2110.10754/) (2021)

## Built on by (most cited first, 10 of 10)

- [MILP-StuDio: MILP Instance Generation via Block Structure Decomposition](https://mlsanity.com/paper/2410.22806/) (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)
- [Multi-task Representation Learning for Mixed Integer Linear Programming](https://mlsanity.com/paper/2412.14409/) (2024)
- [Learning by Analogy: Enhancing Few-Shot Prompting for Math Word Problem Solving with Computational Graph-Based Retrieval](https://mlsanity.com/paper/2411.16454/) (2024)
- [Dynamic Stratified Contrastive Learning with Upstream Augmentation for MILP Branching](https://mlsanity.com/paper/2511.21107/) (2025)
- [MILP-Evo: Closed-Loop Fully Automatic Design of MILP Solvers](https://mlsanity.com/paper/2607.18252/) (2026)
- [FMIP: Joint Continuous-Integer Flow For Mixed-Integer Linear Programming](https://mlsanity.com/paper/2507.23390/) (2025)
- [SHSP: Structure-Aware Hierarchical Solution Prediction for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2608.25282/) (2026)
- [Reformulation-Contrastive Learning for Mixed Integer Programs](https://mlsanity.com/paper/2610.00730/) (2026)

## Abstract (arXiv)

Recent advancements have introduced machine learning frameworks to enhance the Branch and Bound (B&B) branching policies for solving Mixed Integer Linear Programming (MILP). These methods, primarily relying on imitation learning of Strong Branching, have shown superior performance. However, collecting expert samples for imitation learning, particularly for Strong Branching, is a time-consuming endeavor. To address this challenge, we propose Contrastive Learning with Augmented MILPs for Branching (CAMBranch), a framework that generates Augmented MILPs (AMILPs) by applying variable shifting to limited expert data from their original MILPs. This approach enables the acquisition of a considerable number of labeled expert samples. CAMBranch leverages both MILPs and AMILPs for imitation learning and employs contrastive learning to enhance the model's ability to capture MILP features, thereby improving the quality of branching decisions. Experimental results demonstrate that CAMBranch, trained with only 10% of the complete dataset, exhibits superior performance. Ablation studies further validate the effectiveness of our method.