SEVERAL SPECIAL FUNCTIONS IN FRACTALS AND APPLICATIONS OF THE FRACTAL IN MACHINE LEARNING

Jun Wang, Lei Cao, Xiliang Chen, Wei Tang and Zhixiong Xu
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Jun Wang: Army Engineering University of PLA, Nanjing 211101, P. R. China†Troops of 78092, Chengdu 610031, P. R. China
Lei Cao: Army Engineering University of PLA, Nanjing 211101, P. R. China†Troops of 78092, Chengdu 610031, P. R. China
Xiliang Chen: Army Engineering University of PLA, Nanjing 211101, P. R. China†Troops of 78092, Chengdu 610031, P. R. China
Wei Tang: Army Engineering University of PLA, Nanjing 211101, P. R. China†Troops of 78092, Chengdu 610031, P. R. China
Zhixiong Xu: ��Army Academy of Border and Coastal Defence, Xi’an 710100, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-9

Abstract: The focus of this paper is to study unbounded variation functions from the perspective of Hölder conditions. Three special unbounded variation functions have been constructed. The first is a continuous function of unbounded variation that satisfies the Hölder condition of a given order and the second is a continuous function of unbounded variation that does not satisfy the Hölder condition of any order. The third is a continuous function of unbounded variation defined on any sub-interval of the interval I. Then, specific fractal dimension analysis of the above functions and relevant conclusions have been investigated. Finally, combining functional analysis and reinforcement learning, the convergence of reinforcement learning algorithms can be proved in unified framework.

Keywords: Unbounded Variation; Continuous Function; Machine Learning; Fractals (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500311

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