Multi-objective Portfolio Optimization Via Gradient Descent

TL;DR

This paper presents a flexible, gradient descent-based framework for multi-objective portfolio optimization that handles complex constraints and diverse objectives, outperforming traditional methods in scalability and adaptability.

Contribution

Introduces a novel benchmark framework for multi-objective portfolio optimization using gradient descent with automatic differentiation, supporting complex constraints and multiple objectives.

Findings

Achieves competitive performance against standard solvers.

Supports diverse objectives like CVaR minimization and Sharpe ratio maximization.

Handles complex real-world constraints effectively.

Abstract

Traditional approaches to portfolio optimization, often rooted in Modern Portfolio Theory and solved via quadratic programming or evolutionary algorithms, struggle with scalability or flexibility, especially in scenarios involving complex constraints, large datasets and/or multiple conflicting objectives. To address these challenges, we introduce a benchmark framework for multi-objective portfolio optimization (MPO) using gradient descent with automatic differentiation. Our method supports any optimization objective, such as minimizing risk measures (e.g., CVaR) or maximizing Sharpe ratio, along with realistic constraints, such as tracking error limits, UCITS regulations, or asset group restrictions. We have evaluated our framework across six experimental scenarios, from single-objective setups to complex multi-objective cases, and have compared its performance against standard solvers like CVXPY and SKFOLIO. Our results show that our method achieves competitive performance while offering enhanced flexibility for modeling multiple objectives and constraints. We aim to provide a practical and extensible tool for researchers and practitioners exploring advanced portfolio optimization problems in real-world conditions.