# Large-scale portfolio optimization with variational neural annealing

arXiv: https://arxiv.org/abs/2507.07159 · HTML: https://mlsanity.com/paper/2507.07159/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 83 references that are in the map.
- First posted on arXiv 9 Jul 2025.

## Builds on (most cited first, 20 of 20)

- [Large Language Models in Finance: A Survey](https://mlsanity.com/paper/2311.10723/) (2023)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [Challenges and Opportunities in Quantum Optimization](https://mlsanity.com/paper/2312.02279/) (2023)
- [Dynamic Portfolio Optimization with Real Datasets Using Quantum Processors and Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/2007.00017/) (2020)
- [An adaptive augmented Lagrangian method for training physics and equality constrained artificial neural networks](https://mlsanity.com/paper/2306.04904/) (2023)
- [Learning Constrained Optimization with Deep Augmented Lagrangian Methods](https://mlsanity.com/paper/2403.03454/) (2024)
- [Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer](https://mlsanity.com/paper/1508.06182/) (2015)
- [StockGPT: A GenAI Model for Stock Prediction and Trading](https://mlsanity.com/paper/2404.05101/) (2024)
- [From Deep Learning to LLMs: A survey of AI in Quantitative Investment](https://mlsanity.com/paper/2503.21422/) (2025)
- [Recurrent neural network wave functions for Rydberg atom arrays on kagome lattice](https://mlsanity.com/paper/2405.20384/) (2024)
- [Supplementing Recurrent Neural Networks with Annealing to Solve Combinatorial Optimization Problems](https://mlsanity.com/paper/2207.08189/) (2022)
- [Investigating Topological Order using Recurrent Neural Networks](https://mlsanity.com/paper/2303.11207/) (2023)
- [From Portfolio Optimization to Quantum Blockchain and Security: A Systematic Review of Quantum Computing in Finance](https://mlsanity.com/paper/2307.01155/) (2023)
- [Message Passing Variational Autoregressive Network for Solving Intractable Ising Models](https://mlsanity.com/paper/2404.06225/) (2024)
- [MILLION: A General Multi-Objective Framework with Controllable Risk for Portfolio Management](https://mlsanity.com/paper/2412.03038/) (2024)
- [E2EAI: End-to-End Deep Learning Framework for Active Investing](https://mlsanity.com/paper/2305.16364/) (2023)
- [Advancing Investment Frontiers: Industry-grade Deep Reinforcement Learning for Portfolio Optimization](https://mlsanity.com/paper/2403.07916/) (2024)
- [Lattice Protein Folding with Variational Annealing](https://mlsanity.com/paper/2502.20632/) (2025)
- [Tax-Aware Portfolio Construction via Convex Optimization](https://mlsanity.com/paper/2008.04985/) (2020)

## Abstract (arXiv)

Portfolio optimization is a routine asset management operation conducted in financial institutions around the world. However, under real-world constraints such as turnover limits and transaction costs, its formulation becomes a mixed-integer nonlinear program that current mixed-integer optimizers often struggle to solve. We propose mapping this problem onto a classical Ising-like Hamiltonian and solving it with Variational Neural Annealing (VNA), via its classical formulation implemented using autoregressive neural networks. We demonstrate that VNA can identify near-optimal solutions for portfolios comprising more than 2,000 assets and yields performance comparable to that of state-of-the-art optimizers, such as Mosek, while exhibiting faster convergence on hard instances. Finally, we present a dynamical finite-size scaling analysis applied to the S&P 500, Russell 1000, and Russell 3000 indices, revealing universal behavior and polynomial annealing time scaling of the VNA algorithm on portfolio optimization problems.