# Optimization Problems for Machine Learning: A Survey

arXiv: https://arxiv.org/abs/1901.05331 · HTML: https://mlsanity.com/paper/1901.05331/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2019.

## Built on by (most cited first, 15 of 15)

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- [Global Optimization: A Machine Learning Approach](https://mlsanity.com/paper/2311.01742/) (2023)
- [Feed-Forward Neural Networks as a Mixed-Integer Program](https://mlsanity.com/paper/2402.06697/) (2024)
- [A reinforcement learning approach to resource allocation in genomic selection](https://mlsanity.com/paper/2107.10901/) (2021)
- [AutoDOViz: Human-Centered Automation for Decision Optimization](https://mlsanity.com/paper/2302.09688/) (2023)
- [Support Vector Machines with the Hard-Margin Loss: Optimal Training via Combinatorial Benders' Cuts](https://mlsanity.com/paper/2207.07690/) (2022)
- [Machine Learning Models Disclosure from Trusted Research Environments (TRE), Challenges and Opportunities](https://mlsanity.com/paper/2111.05628/) (2021)
- [Strong bounds for large-scale Minimum Sum-of-Squares Clustering](https://mlsanity.com/paper/2502.08397/) (2025)
- [Optimizing accuracy and diversity: a multi-task approach to forecast combinations](https://mlsanity.com/paper/2310.20545/) (2023)

## Abstract (arXiv)

This paper surveys the machine learning literature and presents in an optimization framework several commonly used machine learning approaches. Particularly, mathematical optimization models are presented for regression, classification, clustering, deep learning, and adversarial learning, as well as new emerging applications in machine teaching, empirical model learning, and Bayesian network structure learning. Such models can benefit from the advancement of numerical optimization techniques which have already played a distinctive role in several machine learning settings. The strengths and the shortcomings of these models are discussed and potential research directions and open problems are highlighted.