{"ID":2896709,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.07159","arxiv_id":"2507.07159","title":"Large-scale portfolio optimization with variational neural annealing","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\u0026P 500, Russell 1000, and Russell 3000 indices, revealing universal behavior and polynomial annealing time scaling of the VNA algorithm on portfolio optimization problems.","short_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 solv...","url_abs":"https://arxiv.org/abs/2507.07159","url_pdf":"https://arxiv.org/pdf/2507.07159v1","authors":"[\"Nishan Ranabhat\",\"Behnam Javanparast\",\"David Goerz\",\"Estelle Inack\"]","published":"2025-07-09T17:46:59Z","proceeding":"cond-mat.dis-nn","tasks":"[\"cond-mat.dis-nn\",\"cond-mat.stat-mech\",\"cs.LG\",\"q-fin.PM\"]","methods":"[]","has_code":false}