标题： 基于梯度下降的多目标投资组合优化 显示英文标题

标题： Multi-objective Portfolio Optimization Via Gradient Descent

摘要： 传统投资组合优化方法，通常基于现代投资组合理论，并通过二次规划或进化算法求解，在可扩展性或灵活性方面存在困难，特别是在涉及复杂约束、大规模数据集和/或多个冲突目标的场景中。 为解决这些挑战，我们引入了一个用于多目标投资组合优化（MPO）的基准框架，该框架使用带有自动微分的梯度下降法。 我们的方法支持任何优化目标，例如最小化风险度量（如CVaR）或最大化夏普比率，同时结合现实约束，例如跟踪误差限制、UCITS法规或资产组限制。 我们在六个实验场景中评估了我们的框架，从单目标设置到复杂的多目标情况，并将其性能与标准求解器如CVXPY和SKFOLIO进行了比较。 我们的结果表明，我们的方法在保持竞争力的同时，为建模多个目标和约束提供了增强的灵活性。 我们旨在为研究人员和从业者提供一个实用且可扩展的工具，以探索现实条件下的高级投资组合优化问题。 显示英文摘要

摘要： 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.