Machine Learning Optimization Algorithms & Portfolio Allocation

66 Pages Posted: 25 Jul 2019

See all articles by Sarah Perrin

Sarah Perrin

University of Paris-Saclay - Ecole Polytechnique

Thierry Roncalli

Amundi Asset Management; University of Evry

Date Written: July 1, 2019


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 (Michaud, 1989). 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 and branch of science has faced similar issues concerning large-scale optimization problems. Machine learning and applied statistics have 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. This paper reviews them and shows how they can be implemented in portfolio allocation.

Keywords: portfolio allocation, mean-variance optimization, risk budgeting optimization, quadratic programming, coordinate descent, alternating direction method of multipliers, proximal gradient method, Dykstra's algorithm

JEL Classification: C61, G11

Suggested Citation

Perrin, Sarah and Roncalli, Thierry, Machine Learning Optimization Algorithms & Portfolio Allocation (July 1, 2019). Available at SSRN: or

Sarah Perrin

University of Paris-Saclay - Ecole Polytechnique ( email )

55 Avenue de Paris
Versailles, 78000

Thierry Roncalli (Contact Author)

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015

University of Evry ( email )

Boulevard Francois Mitterrand
F-91025 Evry Cedex

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