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April 2016 Multi-level stochastic approximation algorithms
Noufel Frikha
Ann. Appl. Probab. 26(2): 933-985 (April 2016). DOI: 10.1214/15-AAP1109


This paper studies multi-level stochastic approximation algorithms. Our aim is to extend the scope of the multi-level Monte Carlo method recently introduced by Giles [Oper. Res. 56 (2008) 607–617] to the framework of stochastic optimization by means of stochastic approximation algorithm. We first introduce and study a two-level method, also referred as statistical Romberg stochastic approximation algorithm. Then its extension to a multi-level method is proposed. We prove a central limit theorem for both methods and give optimal parameters. Numerical results confirm the theoretical analysis and show a significant reduction in the initial computational cost.


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Noufel Frikha. "Multi-level stochastic approximation algorithms." Ann. Appl. Probab. 26 (2) 933 - 985, April 2016.


Received: 1 October 2013; Revised: 1 February 2015; Published: April 2016
First available in Project Euclid: 22 March 2016

zbMATH: 1344.93111
MathSciNet: MR3476630
Digital Object Identifier: 10.1214/15-AAP1109

Primary: 60F05, 60H35, 62K12, 65C05

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.26 • No. 2 • April 2016
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