An Improvement of Stochastic Gradient Descent Approach for Mean-Variance Portfolio Optimization Problem

In this paper, the current variant technique of the stochastic gradient descent (SGD) approach, namely, the adaptive moment estimation (Adam) approach, is improved by adding the standard error in the updating rule. The aim is to fasten the convergence rate of the Adam algorithm. This improvement is...

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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2021, Vol.2021, p.1-10
Main Authors: Su, Stephanie S. W., Kek, Sie Long
Format: Article
Language:English
Subjects:
Algorithms
Bias
Convergence
Iterative methods
Iterative solution
Lagrange multiplier
Mathematics
Mean
Money markets
Optimization
Standard error
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Summary:In this paper, the current variant technique of the stochastic gradient descent (SGD) approach, namely, the adaptive moment estimation (Adam) approach, is improved by adding the standard error in the updating rule. The aim is to fasten the convergence rate of the Adam algorithm. This improvement is termed as Adam with standard error (AdamSE) algorithm. On the other hand, the mean-variance portfolio optimization model is formulated from the historical data of the rate of return of the S&P 500 stock, 10-year Treasury bond, and money market. The application of SGD, Adam, adaptive moment estimation with maximum (AdaMax), Nesterov-accelerated adaptive moment estimation (Nadam), AMSGrad, and AdamSE algorithms to solve the mean-variance portfolio optimization problem is further investigated. During the calculation procedure, the iterative solution converges to the optimal portfolio solution. It is noticed that the AdamSE algorithm has the smallest iteration number. The results show that the rate of convergence of the Adam algorithm is significantly enhanced by using the AdamSE algorithm. In conclusion, the efficiency of the improved Adam algorithm using the standard error has been expressed. Furthermore, the applicability of SGD, Adam, AdaMax, Nadam, AMSGrad, and AdamSE algorithms in solving the mean-variance portfolio optimization problem is validated.
ISSN:2314-4629
2314-4785
DOI:10.1155/2021/8892636