Fractional Stochastic Search Algorithms: Modelling Complex Systems via AI

Bodo Herzog

Mathematics, 2023, vol. 11, issue 9, 1-11

Abstract: The aim of this article is to establish a stochastic search algorithm for neural networks based on the fractional stochastic processes { B t H , t ≥ 0 } with the Hurst parameter H ∈ ( 0 , 1 ) . We define and discuss the properties of fractional stochastic processes, { B t H , t ≥ 0 } , which generalize a standard Brownian motion. Fractional stochastic processes capture useful yet different properties in order to simulate real-world phenomena. This approach provides new insights to stochastic gradient descent (SGD) algorithms in machine learning. We exhibit convergence properties for fractional stochastic processes.

Keywords: fractional Brownian motion; fractional stochastic gradient descent; machine learning; stochastic gradient descent; complex systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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