# Differentiable Cutting-plane Layers for Mixed-integer Linear Optimization

arXiv: https://arxiv.org/abs/2311.03350 · HTML: https://mlsanity.com/paper/2311.03350/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 67 references that are in the map.
- First posted on arXiv 6 Nov 2023.

## Builds on (most cited first, 24 of 24)

- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Reinforcement Learning for Integer Programming: Learning to Cut](https://mlsanity.com/paper/1906.04859/) (2019)
- [Parallelizing the dual revised simplex method](https://mlsanity.com/paper/1503.01889/) (2015)
- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)
- [Differentiating Through a Cone Program](https://mlsanity.com/paper/1904.09043/) (2019)
- [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)
- [Online Mixed-Integer Optimization in Milliseconds](https://mlsanity.com/paper/1907.02206/) (2019)
- [Learning Convex Optimization Control Policies](https://mlsanity.com/paper/1912.09529/) (2019)
- [Learning with Combinatorial Optimization Layers: a Probabilistic Approach](https://mlsanity.com/paper/2207.13513/) (2022)
- [The Voice of Optimization](https://mlsanity.com/paper/1812.09991/) (2018)
- [Adaptive Cut Selection in Mixed-Integer Linear Programming](https://mlsanity.com/paper/2202.10962/) (2022)
- [Machine Learning for Cutting Planes in Integer Programming: A Survey](https://mlsanity.com/paper/2302.09166/) (2023)
- [Warm Start of Mixed-Integer Programs for Model Predictive Control of Hybrid Systems](https://mlsanity.com/paper/1910.08251/) (2019)
- [Theoretical challenges towards cutting-plane selection](https://mlsanity.com/paper/1805.02782/) (2018)
- [CoCo: Online Mixed-Integer Control via Supervised Learning](https://mlsanity.com/paper/2107.08143/) (2021)
- [Learning to Use Local Cuts](https://mlsanity.com/paper/2206.11618/) (2022)
- [Continuous cutting plane algorithms in integer programming](https://mlsanity.com/paper/2204.09122/) (2022)
- [Cutting Plane Selection with Analytic Centers and Multiregression](https://mlsanity.com/paper/2212.07231/) (2022)
- [Progressively Strengthening and Tuning MIP Solvers for Reoptimization](https://mlsanity.com/paper/2308.08986/) (2023)
- [Disjunctive cuts in Mixed-Integer Conic Optimization](https://mlsanity.com/paper/1912.03166/) (2019)

## Built on by (most cited first, 3 of 3)

- [Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guarantees](https://mlsanity.com/paper/2410.11061/) (2024)
- [Learn2Aggregate: Supervised Generation of Chv'atal-Gomory Cuts Using Graph Neural Networks](https://mlsanity.com/paper/2409.06559/) (2024)
- [The Differentiable Feasibility Pump](https://mlsanity.com/paper/2411.03535/) (2024)

## Abstract (arXiv)

We consider the problem of solving a family of parametric mixed-integer linear optimization problems where some entries in the input data change. We introduce the concept of cutting-plane layer (CPL), i.e., a differentiable cutting-plane generator mapping the problem data and previous iterates to cutting planes. We propose a CPL implementation to generate split cuts, and by combining several CPLs, we devise a differentiable cutting-plane algorithm that exploits the repeated nature of parametric instances. In an offline phase, we train our algorithm by updating the internal parameters controlling the CPLs, thus altering cut generation. Once trained, our algorithm computes, with predictable execution times and a fixed number of cuts, solutions with low integrality gaps. Preliminary computational tests show that our algorithm generalizes on unseen instances and captures underlying parametric structures.