Beck, Christian; Jentzen, Arnulf; Kleinberg, Konrad; Kruse, Thomas Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems. arXiv:2303.03390 Preprint, arXiv:2303.03390 [math.OC] (2023). MSC: 90C40 90C39 60J05 93E20 65C05 BibTeX Cite \textit{C. Beck} et al., ``Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems'', Preprint, arXiv:2303.03390 [math.OC] (2023) Full Text: arXiv OA License
Cheridito, Patrick; Jentzen, Arnulf; Rossmannek, Florian Landscape analysis for shallow neural networks: complete classification of critical points for affine target functions. (English) Zbl 1491.68179 J. Nonlinear Sci. 32, No. 5, Paper No. 64, 45 p. (2022). MSC: 68T07 90C26 PDFBibTeX XMLCite \textit{P. Cheridito} et al., J. Nonlinear Sci. 32, No. 5, Paper No. 64, 45 p. (2022; Zbl 1491.68179) Full Text: DOI arXiv
Jentzen, Arnulf; Kuckuck, Benno; Neufeld, Ariel; von Wurstemberger, Philippe Strong error analysis for stochastic gradient descent optimization algorithms. (English) Zbl 1460.65071 IMA J. Numer. Anal. 41, No. 1, 455-492 (2021). MSC: 65K05 90C15 PDFBibTeX XMLCite \textit{A. Jentzen} et al., IMA J. Numer. Anal. 41, No. 1, 455--492 (2021; Zbl 1460.65071) Full Text: DOI arXiv
Fehrman, Benjamin; Gess, Benjamin; Jentzen, Arnulf Convergence rates for the stochastic gradient descent method for non-convex objective functions. (English) Zbl 1520.68143 J. Mach. Learn. Res. 21, Paper No. 136, 48 p. (2020). MSC: 68T05 65K05 90C15 90C26 PDFBibTeX XMLCite \textit{B. Fehrman} et al., J. Mach. Learn. Res. 21, Paper No. 136, 48 p. (2020; Zbl 1520.68143) Full Text: arXiv Link
Jentzen, Arnulf; von Wurstemberger, Philippe Lower error bounds for the stochastic gradient descent optimization algorithm: sharp convergence rates for slowly and fast decaying learning rates. (English) Zbl 1433.68353 J. Complexity 57, Article ID 101438, 16 p. (2020). MSC: 68T05 68Q17 90C15 90C52 PDFBibTeX XMLCite \textit{A. Jentzen} and \textit{P. von Wurstemberger}, J. Complexity 57, Article ID 101438, 16 p. (2020; Zbl 1433.68353) Full Text: DOI arXiv