Review Articles

## Research on three-step accelerated gradient algorithm in deep learning

Yongqiang Lian ,

KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai, People’s Republic of China

Yincai Tang ,

KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai, People’s Republic of China

Shirong Zhou

KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai, People’s Republic of China

Pages 40-57 | Received 04 Jun. 2020, Accepted 02 Nov. 2020, Published online: 23 Nov. 2020,
• Abstract
• References
• Citations

Gradient descent (GD) algorithm is the widely used optimisation method in training machine learning and deep learning models. In this paper, based on GD, Polyak’s momentum (PM), and Nesterov accelerated gradient (NAG), we give the convergence of the algorithms from an initial value to the optimal value of an objective function in simple quadratic form. Based on the convergence property of the quadratic function, two sister sequences of NAG’s iteration and parallel tangent methods in neural networks, the three-step accelerated gradient (TAG) algorithm is proposed, which has three sequences other than two sister sequences. To illustrate the performance of this algorithm, we compare the proposed algorithm with the three other algorithms in quadratic function, high-dimensional quadratic functions, and nonquadratic function. Then we consider to combine the TAG algorithm to the backpropagation algorithm and the stochastic gradient descent algorithm in deep learning. For convenientlyfacilitate the proposed algorithms, we rewite the R package ‘neuralnet’ and extend it to ‘supneuralnet’. All kinds of deep learning

algorithms in this paper are included in ‘supneuralnet’ package. Finally, we show our algorithms are superior to other algorithms in four case studies.

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To cite this article: Yongqiang Lian, Yincai Tang & Shirong Zhou (2020): Research on threestep
accelerated gradient algorithm in deep learning, Statistical Theory and Related Fields, DOI:
10.1080/24754269.2020.1846414