# Machine Learning Optimization Algorithms & Portfolio Allocation

arXiv: https://arxiv.org/abs/1909.10233 · HTML: https://mlsanity.com/paper/1909.10233/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2019.

## Built on by (most cited first, 6 of 6)

- [AI in Finance: Challenges, Techniques and Opportunities](https://mlsanity.com/paper/2107.09051/) (2021)
- [Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications](https://mlsanity.com/paper/2307.00908/) (2023)
- [On Evaluating Loss Functions for Stock Ranking: An Empirical Analysis With Transformer Model](https://mlsanity.com/paper/2510.14156/) (2025)
- [Fusion of Sentiment and Asset Price Predictions for Portfolio Optimization](https://mlsanity.com/paper/2203.05673/) (2022)
- [Optimal Linear Signal: An Unsupervised Machine Learning Framework to Optimize PnL with Linear Signals](https://mlsanity.com/paper/2401.05337/) (2023)
- [Enhancing Portfolio Optimization with Deep Learning Insights](https://mlsanity.com/paper/2601.07942/) (2026)

## Abstract (arXiv)

Portfolio optimization emerged with the seminal paper of Markowitz (1952). The original mean-variance framework is appealing because it is very efficient from a computational point of view. However, it also has one well-established failing since it can lead to portfolios that are not optimal from a financial point of view. Nevertheless, very few models have succeeded in providing a real alternative solution to the Markowitz model. The main reason lies in the fact that most academic portfolio optimization models are intractable in real life although they present solid theoretical properties. By intractable we mean that they can be implemented for an investment universe with a small number of assets using a lot of computational resources and skills, but they are unable to manage a universe with dozens or hundreds of assets. However, the emergence and the rapid development of robo-advisors means that we need to rethink portfolio optimization and go beyond the traditional mean-variance optimization approach. Another industry has faced similar issues concerning large-scale optimization problems. Machine learning has long been associated with linear and logistic regression models. Again, the reason was the inability of optimization algorithms to solve high-dimensional industrial problems. Nevertheless, the end of the 1990s marked an important turning point with the development and the rediscovery of several methods that have since produced impressive results. The goal of this paper is to show how portfolio allocation can benefit from the development of these large-scale optimization algorithms. Not all of these algorithms are useful in our case, but four of them are essential when solving complex portfolio optimization problems. These four algorithms are the coordinate descent, the alternating direction method of multipliers, the proximal gradient method and the Dykstra's algorithm.