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arXiv · 2507.07159

Large-scale portfolio optimization with variational neural annealing

Nishan Ranabhat·Behnam Javanparast·David Goerz·Estelle Inack
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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.

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Nishan Ranabhat, Behnam Javanparast, David Goerz, Estelle Inack. 2025-07-09. Large-scale portfolio optimization with variational neural annealing. https://doi.org/10.1103/p22k-x7p6

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