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In the recent years, various gradient descent algorithms including themethods of gradient descent, gradient descent with momentum, adaptive gradient(AdaGrad), root-mean-square propagation (RMSProp) and adaptive momentestimation (Adam) have been applied to the parameter optimization of severaldeep learning models with higher accuracies or lower errors. These optimizationalgorithms may need to set the values of several hyperparameters which includea learning rate, momentum coefficients, etc. Furthermore, the convergence speedand solution accuracy may be influenced by the values of hyperparameters.Therefore, this study proposes an analytical framework to use mathematicalmodels for analyzing the mean error of each objective function based on variousgradient descent algorithms. Moreover, the suitable value of eachhyperparameter could be determined by minimizing the mean error. The principlesof hyperparameter value setting have been generalized based on analysis resultsfor model optimization. The experimental results show that higher efficiencyconvergences and lower errors can be obtained by the proposed method.

Exploring the Optimized Value of Each Hyperparameter in Various Gradient Descent Algorithms