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Volume 8
Issue 3
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Article

Accelerated Gradient Descent Driven by Lévy Perturbations

by
Yuquan Chen
1,*,
Zhenlong Wu
2,
Yixiang Lu
3,
Yangquan Chen
4 and
Yong Wang
5
1
Department of Automation, Hohai University, Nanjing 210024, China
2
School of Electrical Engineering, Zhengzhou University, Zhengzhou 450001, China
3
Anhui Engineering Laboratory of Human Robot Integration System and Equipment, School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China
4
School of Engineering, University of California, Merced, CA 95343, USA
5
Department of Automation, University of Science and Technology of China, Hefei 230026, China
*
Author to whom correspondence should be addressed.
Fractal Fract. 2024, 8(3), 170; https://doi.org/10.3390/fractalfract8030170
Submission received: 17 January 2024 / Revised: 1 March 2024 / Accepted: 12 March 2024 / Published: 14 March 2024
(This article belongs to the Special Issue Fractional Calculus in Signal, Imaging Processing and Machine Learning)
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Abstract

In this paper, we mainly consider two kinds of perturbed accelerated gradient descents driven by Lévy perturbations, which is of great importance for enhancing the global search ability. By using Lévy representation, Lévy perturbations can be divided into two parts: small jumps and large jumps, whose properties are then carefully discussed. By introducing the concept of attraction domain for local minima, Makovian transition properties are proven for the proposed two perturbed accelerated gradient descents with different infinitesimal matrices. Finally, all the results are extended to the vector case and two simulation examples are provided to validate all the conclusions.
Keywords: accelerated gradient descent; Lévy perturbations; global optimization; Markovian transition property accelerated gradient descent; Lévy perturbations; global optimization; Markovian transition property

Share and Cite

MDPI and ACS Style

Chen, Y.; Wu, Z.; Lu, Y.; Chen, Y.; Wang, Y. Accelerated Gradient Descent Driven by Lévy Perturbations. Fractal Fract. 2024, 8, 170. https://doi.org/10.3390/fractalfract8030170

AMA Style

Chen Y, Wu Z, Lu Y, Chen Y, Wang Y. Accelerated Gradient Descent Driven by Lévy Perturbations. Fractal and Fractional. 2024; 8(3):170. https://doi.org/10.3390/fractalfract8030170

Chicago/Turabian Style

Chen, Yuquan, Zhenlong Wu, Yixiang Lu, Yangquan Chen, and Yong Wang. 2024. "Accelerated Gradient Descent Driven by Lévy Perturbations" Fractal and Fractional 8, no. 3: 170. https://doi.org/10.3390/fractalfract8030170

APA Style

Chen, Y., Wu, Z., Lu, Y., Chen, Y., & Wang, Y. (2024). Accelerated Gradient Descent Driven by Lévy Perturbations. Fractal and Fractional, 8(3), 170. https://doi.org/10.3390/fractalfract8030170

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