用神经退火算法高效求解超大规模投资组合优化问题。
Large-scale portfolio optimization with variational neural annealing
- 将投资组合问题映射为伊辛模型，用自回归神经网络实现变分神经退火。
- 在2000+资产规模下接近最优，收敛速度优于Mosek等主流求解器。
- 揭示了算法在不同指数上的普适行为和多项式退火时间特性，适合金融量化研究者。
投资组合优化是全球金融机构的常规操作，但在换手率限制和交易成本等现实约束下，其数学形式变为混合整数非线性规划，现有求解器常难以应对。本文提出将该问题映射到类伊辛哈密顿量，并通过基于自回归神经网络的变分神经退火（VNA）进行求解。实验表明，VNA能在超过2000个资产的组合上找到近优解，性能媲美Mosek等先进优化器，且在困难实例上收敛更快。进一步对S&P 500、Russell 1000和Russell 3000指数进行动态有限尺寸标度分析，发现算法表现出普适行为，并呈现多项式退火时间缩放规律。
原文摘要 · Abstract (English)
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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