Convergence of Constant Step Stochastic Gradient Descent for Non-Smooth Non-Convex Functions

This paper studies the asymptotic behavior of the constant step Stochastic Gradient Descent for the minimization of an unknown function, defined as the expectation of a non convex, non smooth, locally Lipschitz random function. As the gradient may not exist, it is replaced by a certain operator: a r...

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Bibliographic Details
Published in:	Set-valued and variational analysis Vol. 30; no. 3; pp. 1117 - 1147
Main Authors:	Bianchi, Pascal, Hachem, Walid, Schechtman, Sholom
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 01.09.2022 Springer Nature B.V Springer
Subjects:	Algorithms Analysis Asymptotic properties Back propagation Convergence Critical point Invariants Kernels Markov chains Mathematics Mathematics and Statistics Numerical Analysis Operators (mathematics) Optimization Optimization and Control Probability theory Clarke subdifferential Backpropagation algorithm Differential inclusions 65K05 Stochastic approximation 65K10 Non convex and non smooth optimization 90C15 34A60
ISSN:	1877-0533, 1877-0541
Online Access:	Get full text
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