Large-scale portfolio optimization with variational neural annealing

TL;DR

This paper introduces Variational Neural Annealing (VNA), a neural network-based approach that efficiently solves large-scale, constrained portfolio optimization problems, achieving near-optimal solutions faster than traditional methods.

Contribution

It presents a novel neural annealing method mapping portfolio optimization to an Ising-like Hamiltonian, capable of handling over 2,000 assets with performance comparable to state-of-the-art solvers.

Findings

VNA finds near-optimal solutions for large portfolios.

VNA converges faster than traditional optimizers on hard instances.

Universal scaling behavior observed in VNA performance across different indices.

Abstract

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.