# Optimization Problems for Machine Learning: A Survey

## TL;DR

This survey reviews how various machine learning methods can be formulated as optimization problems, highlighting recent advances, challenges, and future research directions in the field.

## Contribution

It provides a comprehensive overview of optimization models across multiple machine learning approaches and discusses their strengths, limitations, and emerging applications.

## Key findings

- Optimization models enhance machine learning techniques.
- Numerical optimization advances benefit various ML applications.
- Open problems and future research directions are identified.

## Abstract

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.