[论文解读] Machine Learning Optimization Algorithms & Portfolio Allocation

Sarah Perrin, Thierry Roncalli|arXiv (Cornell University)|Jan 1, 2019

Stochastic Gradient Optimization Techniques参考文献 58被引用 7

一句话总结

本文提出利用现代大规模机器学习优化算法——坐标下降法、ADMM、近端梯度法以及Dykstra算法——以克服传统均值-方差投资组合优化的局限性，实现大规模投资组合的稳健、可扩展且计算可行的资产配置。

ABSTRACT

Portfolio optimization emerged with the seminal paper of Markowitz (1952). The original mean-variance framework is appealing because it is very efficient from a computational point of view. However, it also has one well-established failing since it can lead to portfolios that are not optimal from a financial point of view. Nevertheless, very few models have succeeded in providing a real alternative solution to the Markowitz model. The main reason lies in the fact that most academic portfolio optimization models are intractable in real life although they present solid theoretical properties. By intractable we mean that they can be implemented for an investment universe with a small number of assets using a lot of computational resources and skills, but they are unable to manage a universe with dozens or hundreds of assets. However, the emergence and the rapid development of robo-advisors means that we need to rethink portfolio optimization and go beyond the traditional mean-variance optimization approach. Another industry has faced similar issues concerning large-scale optimization problems. Machine learning has long been associated with linear and logistic regression models. Again, the reason was the inability of optimization algorithms to solve high-dimensional industrial problems. Nevertheless, the end of the 1990s marked an important turning point with the development and the rediscovery of several methods that have since produced impressive results. The goal of this paper is to show how portfolio allocation can benefit from the development of these large-scale optimization algorithms. Not all of these algorithms are useful in our case, but four of them are essential when solving complex portfolio optimization problems. These four algorithms are the coordinate descent, the alternating direction method of multipliers, the proximal gradient method and the Dykstra's algorithm.

研究动机与目标

• 解决在大规模场景下先进投资组合优化模型的计算不可行性问题。
• 识别并适配大规模机器学习优化算法，用于实际投资组合配置。
• 展示这些算法如何在传统均值-方差优化之外提升投资组合优化的稳健性与可扩展性。
• 为现代投资组合管理提供可实施的解决方案，尤其适用于机器人投顾和机构投资者。

提出的方法

• 将坐标下降法应用于求解带有稀疏性诱导惩罚项的正则化投资组合优化问题。
• 采用交替方向乘子法（ADMM）将复杂的投资组合约束分解为可处理的子问题。
• 使用近端梯度法处理风险与收益目标中的非光滑正则化项。
• 将Dykstra算法适配用于求解在风险预算和最小方差投资组合中出现的 bound-constrained quadratic programming 问题。
• 将投资组合优化重新表述为可被这些算法求解的凸优化问题，确保收敛性与可扩展性。
• 将这些方法整合到实际框架中，用于风险预算、最小方差及正则化均值-方差优化。

实验结果

研究问题

• RQ1 大规模机器学习优化算法能否被有效应用于现代投资组合配置问题？
• RQ2 坐标下降法、ADMM、近端梯度法和Dykstra算法如何提升投资组合优化的稳健性与可扩展性？
• RQ3 与传统均值-方差优化相比，使用这些算法在计算与金融方面具有哪些优势？
• RQ4 如何利用这些方法高效实现大规模投资组合问题中的正则化与约束处理？
• RQ5 这些算法能否实现先进投资组合模型在机器人投顾与资产管理中的实际、现实世界部署？

主要发现

• 四种算法——坐标下降法、ADMM、近端梯度法和Dykstra算法——在求解具有复杂约束的大规模投资组合优化问题方面均表现出有效性。
• 这些方法通过引入正则化与风险控制，实现了稳健的投资组合构建，降低了对估计误差的敏感性。
• ADMM与近端方法可将大规模问题分解为更小、可并行处理的子问题，从而提升计算效率。
• Dykstra算法能有效处理最小方差与风险预算投资组合中的边界约束，确保数值稳定性。
• 将这些算法整合到投资组合优化中，可实现可扩展、实时且稳健的资产配置，适用于工业应用。
• 该方法通过提供系统化、非试错式的框架，克服了传统均值-方差优化的局限性，实现了投资组合构建。