# Multi-objective Portfolio Optimization Via Gradient Descent

arXiv: https://arxiv.org/abs/2507.16717 · HTML: https://mlsanity.com/paper/2507.16717/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 36 references that are in the map.
- First posted on arXiv 22 Jul 2025.

## Builds on (most cited first, 5 of 5)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [MILLION: A General Multi-Objective Framework with Controllable Risk for Portfolio Management](https://mlsanity.com/paper/2412.03038/) (2024)

## Built on by (most cited first, 2 of 2)

- [Agentic Trading: When LLM Agents Meet Financial Markets](https://mlsanity.com/paper/2605.19337/) (2026)
- [Complexity Bounds for Smooth Multiobjective Optimization](https://mlsanity.com/paper/2509.13550/) (2025)

## Abstract (arXiv)

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.