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Article Dans Une Revue The Annals of Applied Probability Année : 2016

Multi-level stochastic approximation algorithms

Résumé

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.
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Dates et versions

hal-00870585 , version 1 (07-10-2013)
hal-00870585 , version 2 (06-08-2014)

Identifiants

Citer

Noufel Frikha. Multi-level stochastic approximation algorithms. The Annals of Applied Probability, 2016, 26 (2), pp.933-985. ⟨10.1214/15-AAP1109⟩. ⟨hal-00870585v2⟩
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