# Learning for Spatial Branching: An Algorithm Selection Approach

arXiv: https://arxiv.org/abs/2204.10834 · HTML: https://mlsanity.com/paper/2204.10834/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 48 references that are in the map.
- First posted on arXiv 22 Apr 2022.

## Builds on (most cited first, 8 of 8)

- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (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)
- [Hybrid Models for Learning to Branch](https://mlsanity.com/paper/2006.15212/) (2020)
- [Fast calibrated additive quantile regression](https://mlsanity.com/paper/1707.03307/) (2017)
- [DASH: Dynamic Approach for Switching Heuristics](https://mlsanity.com/paper/1307.4689/) (2013)
- [Some Applications of Polynomial Optimization in Operations Research and Real-Time Decision Making](https://mlsanity.com/paper/1504.06002/) (2015)
- [Extremal Quantile Regression: An Overview](https://mlsanity.com/paper/1612.06850/) (2016)

## Built on by (most cited first, 6 of 6)

- [Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Process](https://mlsanity.com/paper/2401.03244/) (2024)
- [Accelerating process control and optimization via machine learning: A review](https://mlsanity.com/paper/2412.18529/) (2024)
- [NeuralQP: A General Hypergraph-based Optimization Framework for Large-scale QCQPs](https://mlsanity.com/paper/2410.03720/) (2024)
- [Polynomial Optimization: Enhancing RLT relaxations with Conic Constraints](https://mlsanity.com/paper/2208.05608/) (2022)
- [Towards Solving Polynomial-Objective Integer Programming with Hypergraph Neural Networks](https://mlsanity.com/paper/2603.19318/) (2026)
- [Speeding Up Mixed-Integer Programming Solvers with Sparse Learning for Branching](https://mlsanity.com/paper/2604.00094/) (2026)

## Abstract (arXiv)

The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To bridge this gap, we develop a learning framework for spatial branching and show its efficacy in the context of the Reformulation-Linearization Technique for polynomial optimization problems. The proposed learning is performed offline, based on instance-specific features and with no computational overhead when solving new instances. Novel graph-based features are introduced, which turn out to play an important role for the learning. Experiments on different benchmark instances from the literature show that the learning-based branching rule significantly outperforms the standard rules.