# Stochastic Cutting Planes for Data-Driven Optimization

arXiv: https://arxiv.org/abs/2103.02506 · HTML: https://mlsanity.com/paper/2103.02506/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 32 references that are in the map.
- First posted on arXiv 3 Mar 2021.

## Builds on (most cited first, 3 of 3)

- [Sparse High-Dimensional Regression: Exact Scalable Algorithms and Phase Transitions](https://mlsanity.com/paper/1709.10029/) (2017)
- [A unified approach to mixed-integer optimization problems with logical constraints](https://mlsanity.com/paper/1907.02109/) (2019)
- [Interpretable Matrix Completion: A Discrete Optimization Approach](https://mlsanity.com/paper/1812.06647/) (2018)

## Abstract (arXiv)

We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to an ε-optimal solution with high probability. Numerical experiments on several problems show that stochastic cutting planes is able to deliver a multiple order-of-magnitude speedup compared to the standard cutting-plane method. We further experimentally explore the lower limits of sampling for stochastic cutting planes and show that for many problems, a sampling size of O(√[3]n) appears to be sufficient for high quality solutions.