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Recent Advances in Stochastic Gradient Descent in Deep Learning

Author

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  • Yingjie Tian

    (School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, China
    Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Beijing 100190, China
    Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing 100190, China)

  • Yuqi Zhang

    (School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China)

  • Haibin Zhang

    (Beijing Institute for Scientific and Engineering Computing, Faculty of Science, Beijing University of Technology, Beijing 100124, China)

Abstract

In the age of artificial intelligence, the best approach to handling huge amounts of data is a tremendously motivating and hard problem. Among machine learning models, stochastic gradient descent (SGD) is not only simple but also very effective. This study provides a detailed analysis of contemporary state-of-the-art deep learning applications, such as natural language processing (NLP), visual data processing, and voice and audio processing. Following that, this study introduces several versions of SGD and its variant, which are already in the PyTorch optimizer, including SGD, Adagrad, adadelta, RMSprop, Adam, AdamW, and so on. Finally, we propose theoretical conditions under which these methods are applicable and discover that there is still a gap between theoretical conditions under which the algorithms converge and practical applications, and how to bridge this gap is a question for the future.

Suggested Citation

  • Yingjie Tian & Yuqi Zhang & Haibin Zhang, 2023. "Recent Advances in Stochastic Gradient Descent in Deep Learning," Mathematics, MDPI, vol. 11(3), pages 1-23, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:682-:d:1050286
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    References listed on IDEAS

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    1. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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    Cited by:

    1. Rulei Qi & Dan Xue & Yujia Zhai, 2024. "A Momentum-Based Adaptive Primal–Dual Stochastic Gradient Method for Non-Convex Programs with Expectation Constraints," Mathematics, MDPI, vol. 12(15), pages 1-26, July.
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    3. Cong Shen & Wei Zhang & Tanping Zhou & Lingling Zhang, 2024. "A Security-Enhanced Federated Learning Scheme Based on Homomorphic Encryption and Secret Sharing," Mathematics, MDPI, vol. 12(13), pages 1-20, June.
    4. Vasiliki Rokani & Stavros D. Kaminaris & Petros Karaisas & Dimitrios Kaminaris, 2023. "Power Transformer Fault Diagnosis Using Neural Network Optimization Techniques," Mathematics, MDPI, vol. 11(22), pages 1-33, November.

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