In recent years, digital investment portfolios have become a significant area of interest in the field of machine learning. To tackle the issue of neglecting the momentum effect in risk asset prices within the follow-...In recent years, digital investment portfolios have become a significant area of interest in the field of machine learning. To tackle the issue of neglecting the momentum effect in risk asset prices within the follow-the-winner strategy and to evaluate the significance of this effect, a novel measure of risk asset price momentum trend is introduced for online investment portfolio research. Firstly, a novel approach is introduced to quantify the momentum trend effect, which is determined by the product of the slope of the linear regression model and the absolute value of the linear correlation coefficient. Secondly, a new investment portfolio optimization problem is established based on the prediction of future returns. Thirdly, the Lagrange multiplier method is used to obtain the analytical solution of the optimization model, and the soft projection optimization algorithm is used to map the analytical solution to obtain the investment portfolio of the model. Finally, experiments are conducted on five benchmark datasets and compared with popular investment portfolio algorithms. The empirical findings indicate that the algorithm we are introduced is capable of generating higher investment returns, thereby establishing its efficacy for the management of the online investment portfolios.展开更多
随机梯度下降动量法(Stochastic Gradient Descent with Momentum,SGDM)是一种广泛应用于求解机器学习问题的优化方法。该算法通过累积历史梯度来加速训练,但由于噪声的累积可能引发超调现象。基于非线性共轭梯度参数提出了一种自适应...随机梯度下降动量法(Stochastic Gradient Descent with Momentum,SGDM)是一种广泛应用于求解机器学习问题的优化方法。该算法通过累积历史梯度来加速训练,但由于噪声的累积可能引发超调现象。基于非线性共轭梯度参数提出了一种自适应动量的SGDM算法—PRPSGDM,该算法通过自适应调整动量系数,合理控制高噪声梯度在加速下降过程中的影响。此外,还对该算法进行了偏差分析和非凸随机优化问题下的收敛性分析。数值实验验证了算法在求解非凸支持向量机问题下的有效性。展开更多
摘要In recent years, digital investment portfolios have become a significant area of interest in the field of machine learning. To tackle the issue of neglecting the momentum effect in risk asset prices within the follow-the-winner strategy and to evaluate the significance of this effect, a novel measure of risk asset price momentum trend is introduced for online investment portfolio research. Firstly, a novel approach is introduced to quantify the momentum trend effect, which is determined by the product of the slope of the linear regression model and the absolute value of the linear correlation coefficient. Secondly, a new investment portfolio optimization problem is established based on the prediction of future returns. Thirdly, the Lagrange multiplier method is used to obtain the analytical solution of the optimization model, and the soft projection optimization algorithm is used to map the analytical solution to obtain the investment portfolio of the model. Finally, experiments are conducted on five benchmark datasets and compared with popular investment portfolio algorithms. The empirical findings indicate that the algorithm we are introduced is capable of generating higher investment returns, thereby establishing its efficacy for the management of the online investment portfolios.
摘要随机梯度下降动量法(Stochastic Gradient Descent with Momentum,SGDM)是一种广泛应用于求解机器学习问题的优化方法。该算法通过累积历史梯度来加速训练,但由于噪声的累积可能引发超调现象。基于非线性共轭梯度参数提出了一种自适应动量的SGDM算法—PRPSGDM,该算法通过自适应调整动量系数,合理控制高噪声梯度在加速下降过程中的影响。此外,还对该算法进行了偏差分析和非凸随机优化问题下的收敛性分析。数值实验验证了算法在求解非凸支持向量机问题下的有效性。