用梯度下降解决多目标投资组合优化，支持复杂约束与多种目标。
Multi-objective Portfolio Optimization Via Gradient Descent
- 基于自动微分的梯度下降框架，灵活处理多目标与约束。
- 在六种场景下表现媲美传统求解器，兼顾性能与可扩展性。
- 适合研究复杂投资策略或实际金融建模的学者与从业者。
传统投资组合优化方法（如现代投资组合理论）常依赖二次规划或进化算法，面临可扩展性差、灵活性不足的问题，尤其在处理复杂约束、大规模数据及多个冲突目标时。为此，我们提出一个基于梯度下降与自动微分的多目标投资组合优化（MPO）基准框架。该方法可支持任意优化目标（如最小化风险度量如CVaR、最大化夏普比率），并兼容真实约束条件，如跟踪误差上限、UCITS监管要求、资产组限制等。我们在六个实验场景中评估该框架，涵盖单目标到复杂多目标设置，并与标准求解器（如CVXPY和SKFOLIO）进行对比。结果表明，该方法在性能上具有竞争力，同时在建模多目标与约束方面展现出更强的灵活性。我们旨在为研究人员和实践者提供一个实用且可扩展的工具，用于探索真实环境下高级投资组合优化问题。
原文摘要 · Abstract (English)
Traditional approaches to portfolio optimization, often rooted in Modern Portfolio Theory and solved via quadratic programming or evolutionary algorithms, struggle with scalability or flexibility, especially in scenarios involving complex constraints, large datasets and/or multiple conflicting objectives. To address these challenges, we introduce a benchmark framework for multi-objective portfolio optimization (MPO) using gradient descent with automatic differentiation. Our method supports any optimization objective, such as minimizing risk measures (e.g., CVaR) or maximizing Sharpe ratio, along with realistic constraints, such as tracking error limits, UCITS regulations, or asset group restrictions. We have evaluated our framework across six experimental scenarios, from single-objective setups to complex multi-objective cases, and have compared its performance against standard solvers like CVXPY and SKFOLIO. Our results show that our method achieves competitive performance while offering enhanced flexibility for modeling multiple objectives and constraints. We aim to provide a practical and extensible tool for researchers and practitioners exploring advanced portfolio optimization problems in real-world conditions.
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