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Unbiased quasi-hyperbolic nesterov-gradient momentum-based optimizers for accelerating convergence

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Abstract

In the training process of deep learning models, one of the important steps is to choose an appropriate optimizer that directly determines the final performance of the model. Choosing the appropriate direction and step size (i.e. learning rate) of parameter update are decisive factors for optimizers. Previous gradient descent optimizers could be oscillated and fail to converge to a minimum point because they are only sensitive to the current gradient. Momentum-Based Optimizers (MBOs) have been widely adopted recently since they can relieve oscillation to accelerate convergence by using the exponentially decaying average of gradients to fine-tune the direction. However, we find that most of the existing MBOs are biased and inconsistent with the local fastest descent direction resulting in a high number of iterations. To accelerate convergence, we propose an Unbiased strategy to adjust the descent direction of a variety of MBOs. We further propose an Unbiased Quasi-hyperbolic Nesterov-gradient strategy (UQN) by combining our Unbiased strategy with the existing Quasi-hyperbolic and Nesterov-gradient. It makes each update step move in the local fastest descent direction, predicts the future gradient to avoid crossing the minimum point, and reduces gradient variance. We extend our strategies to multiple MBOs and prove the convergence of our strategies. The main experimental results presented in this paper are based on popular neural network models and benchmark datasets. The experimental results demonstrate the effectiveness and universality of our proposed strategies.

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Acknowledgements

The work is partially supported by the National Key Research and Development Program of China (2020YFB1707901), National Natural Science Foundation of China (Nos. 62072088, 61991404), Ten Thousand Talent Program (No. ZX20200035), Liaoning Distinguished Professor (No. XLYC1902057), 111 Project (B16009), and GZU-HKUST Joint Research Collaboration Grant (GZU22EG04).

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Authors and Affiliations

  1. School of Computer Science and Engineering, Northeastern University, 110167, Shenyang, Liaoning, China

    Weiwei Cheng, Xiaochun Yang & Bin Wang

  2. National Frontiers Science Center for Industrial Intelligence and Systems Optimization, N/A, China

    Xiaochun Yang & Bin Wang

  3. Key Laboratory of Data Analytics and Optimization for Smart Industry (Northeastern University), Ministry of Education, N/A, China

    Xiaochun Yang & Bin Wang

  4. Information Hub, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, Guangdong, China

    Wei Wang

  5. The Hong Kong University of Science and Technology, Hong Kong, China

    Wei Wang

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  1. Weiwei Cheng
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  4. Wei Wang
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Contributions

Weiwei Cheng and Xiaochun Yang wrote the main manuscript text and Bin Wang and Wei Wang contributed ideas, prepared Figures 1-9, and proofread the paper. All authors reviewed the manuscript. Weiwei Cheng: School of Computer Science and Engineering, Northeastern University, Shenyang, Liaoning, China. Xiaochun Yang, and Bin Wang: School of Computer Science and Engineering, Northeastern University, Shenyang, Liaoning, China; National Frontiers Science Center for Industrial Intelligence and Systems Optimization; Key Laboratory of Data Analytics and Optimization for Smart Industry (Northeastern University), Ministry of Education, China. Wei Wang: Information Hub, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, Guangdong, China; The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.

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Correspondence to Xiaochun Yang.

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Cheng, W., Yang, X., Wang, B. et al. Unbiased quasi-hyperbolic nesterov-gradient momentum-based optimizers for accelerating convergence. World Wide Web 26, 1323–1344 (2023). https://doi.org/10.1007/s11280-022-01086-3

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