Multi-level stochastic approximation algorithms

Abstract : This paper studies multi-level stochastic approximation algorithms. Our aim is to extend the scope of the multilevel Monte Carlo method recently introduced by Giles (Giles 2008) 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 multi-level is proposed. We prove a central limit theorem for both methods and describe the possible optimal choices of step size sequence. Numerical results confirm the theoretical analysis and show a significant reduction in the initial computational cost.
Type de document :
Article dans une revue
The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2016, 26 (2), pp.933-985. <10.1214/15-AAP1109>
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-00870585
Contributeur : Noufel Frikha <>
Soumis le : mercredi 6 août 2014 - 18:43:15
Dernière modification le : lundi 29 mai 2017 - 14:21:28
Document(s) archivé(s) le : mardi 11 avril 2017 - 18:22:30

Fichiers

MultLevelSA.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

INSMI | UPMC | USPC | PMA

Citation

Noufel Frikha. Multi-level stochastic approximation algorithms. The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2016, 26 (2), pp.933-985. <10.1214/15-AAP1109>. <hal-00870585v2>

Partager

Métriques

Consultations de
la notice

153

Téléchargements du document

90