Year: 2024
Author: Steffen Dereich, Sebastian Kassing
Journal of Machine Learning, Vol. 3 (2024), Iss. 3 : pp. 245–281
Abstract
In this article, we consider convergence of stochastic gradient descent schemes (SGD), including momentum stochastic gradient descent (MSGD), under weak assumptions on the underlying landscape. More explicitly, we show that on the event that the SGD stays bounded we have convergence of the SGD if there is only a countable number of critical points or if the objective function satisfies Łojasiewicz-inequalities around all critical levels as all analytic functions do. In particular, we show that for neural networks with analytic activation function such as softplus, sigmoid and the hyperbolic tangent, SGD converges on the event of staying bounded, if the random variables modelling the signal and response in the training are compactly supported.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jml.240109
Journal of Machine Learning, Vol. 3 (2024), Iss. 3 : pp. 245–281
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 37
Keywords: Stochastic gradient descent Stochastic approximation Robbins-Monro Almost sure convergence Łojasiewicz-inequality.
Author Details
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On the Existence of Minimizers in Shallow Residual ReLU Neural Network Optimization Landscapes
Dereich, Steffen
Jentzen, Arnulf
Kassing, Sebastian
SIAM Journal on Numerical Analysis, Vol. 62 (2024), Iss. 6 P.2640
https://doi.org/10.1137/23M1556241 [Citations: 0]