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Convergence rates for the stochastic gradient descent method for non-convex objective functions

by B. Fehrman and B. Gess and A. Jentzen

(Report number 2019-21)

Abstract
We prove the local convergence to minima and estimates on the rate of convergence for the stochastic gradient descent method in the case of not necessarily globally convex nor contracting objective functions. In particular, the results are applicable to simple objective functions arising in machine learning.

Keywords:

@Techreport{FGJ19_825,
  author = {B. Fehrman and B. Gess and A. Jentzen},
  title = {Convergence rates for the stochastic gradient descent method for non-convex objective functions},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2019-21},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2019/2019-21.pdf },
  year = {2019}
}

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