Convergence Rates for the Stochastic Gradient Descent Method for Non-Convex Objective Functions

Fehrman B, Gess B, Jentzen A (2020)
Journal of Machine Learning Research (JMLR) 21: 1.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Fehrman, Benjamin; Gess, BenjaminUniBi; Jentzen, Arnulf
Abstract / Bemerkung
We prove the convergence to minima and estimates on the rate of convergence for the stochastic gradient descent method in the case of not necessarily locally convex nor contracting objective functions. In particular, the analysis relies on a quantitative use of mini-batches to control the loss of iterates to non-attracted regions. The applicability of the results to simple objective functions arising in machine learning is shown.
Stichworte
stochastic gradient descent; mini-batch algorithm; machine learning; non-convex optimization
Erscheinungsjahr
2020
Zeitschriftentitel
Journal of Machine Learning Research (JMLR)
Band
21
Art.-Nr.
1
ISSN
1532-4435
Page URI
https://pub.uni-bielefeld.de/record/2945624

Zitieren

Fehrman B, Gess B, Jentzen A. Convergence Rates for the Stochastic Gradient Descent Method for Non-Convex Objective Functions. Journal of Machine Learning Research (JMLR) . 2020;21: 1.
Fehrman, B., Gess, B., & Jentzen, A. (2020). Convergence Rates for the Stochastic Gradient Descent Method for Non-Convex Objective Functions. Journal of Machine Learning Research (JMLR) , 21, 1
Fehrman, B., Gess, B., and Jentzen, A. (2020). Convergence Rates for the Stochastic Gradient Descent Method for Non-Convex Objective Functions. Journal of Machine Learning Research (JMLR) 21:1.
Fehrman, B., Gess, B., & Jentzen, A., 2020. Convergence Rates for the Stochastic Gradient Descent Method for Non-Convex Objective Functions. Journal of Machine Learning Research (JMLR) , 21: 1.
B. Fehrman, B. Gess, and A. Jentzen, “Convergence Rates for the Stochastic Gradient Descent Method for Non-Convex Objective Functions”, Journal of Machine Learning Research (JMLR) , vol. 21, 2020, : 1.
Fehrman, B., Gess, B., Jentzen, A.: Convergence Rates for the Stochastic Gradient Descent Method for Non-Convex Objective Functions. Journal of Machine Learning Research (JMLR) . 21, : 1 (2020).
Fehrman, Benjamin, Gess, Benjamin, and Jentzen, Arnulf. “Convergence Rates for the Stochastic Gradient Descent Method for Non-Convex Objective Functions”. Journal of Machine Learning Research (JMLR) 21 (2020): 1.

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