# Learning to Pivot as a Smart Expert

arXiv: https://arxiv.org/abs/2308.08171 · HTML: https://mlsanity.com/paper/2308.08171/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Aug 2023.

## Built on by (most cited first, 9 of 9)

- [PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programming](https://mlsanity.com/paper/2406.01908/) (2024)
- [Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programs](https://mlsanity.com/paper/2406.05938/) (2024)
- [Towards graph neural networks for provably solving convex optimization problems](https://mlsanity.com/paper/2502.02446/) (2025)
- [BenLOC: A Benchmark for Learning to Configure MIP Optimizers](https://mlsanity.com/paper/2506.02752/) (2025)
- [Solving Integrated Process Planning and Scheduling Problem via Graph Neural Network Based Deep Reinforcement Learning](https://mlsanity.com/paper/2409.00968/) (2024)
- [From Small to Large: A Graph Convolutional Network Approach for Solving Assortment Optimization Problems](https://mlsanity.com/paper/2507.10834/) (2025)
- [FunL2O: LLM-Guided Feature Function Design for Learning to Optimize](https://mlsanity.com/paper/2607.27389/) (2026)
- [Learned Preconditioning for a Primal-Dual Interior-Point Method](https://mlsanity.com/paper/2609.35665/) (2026)
- [Reinforcement Learning to Accelerate Primal-Dual Hybrid Gradient for Linear Programming](https://mlsanity.com/paper/2610.01546/) (2026)

## Abstract (arXiv)

Linear programming has been practically solved mainly by simplex and interior point methods. Compared with the weakly polynomial complexity obtained by the interior point methods, the existence of strongly polynomial bounds for the length of the pivot path generated by the simplex methods remains a mystery. In this paper, we propose two novel pivot experts that leverage both global and local information of the linear programming instances for the primal simplex method and show their excellent performance numerically. The experts can be regarded as a benchmark to evaluate the performance of classical pivot rules, although they are hard to directly implement. To tackle this challenge, we employ a graph convolutional neural network model, trained via imitation learning, to mimic the behavior of the pivot expert. Our pivot rule, learned empirically, displays a significant advantage over conventional methods in various linear programming problems, as demonstrated through a series of rigorous experiments.