A Perturbed Gradient Algorithm in Hilbert Spaces

Abstract : We propose a perturbed gradient algorithm with stochastic noises to solve a general class of optimization problems. We provide a convergence proof for this algorithm, under classical assumptions on the descent direction, and new assumptions on the stochastic noises. Instead of requiring the stochastic noises to correspond to martingale increments, we only require these noises to be asymptotically so. Furthermore, the variance of these noises is allowed to grow infinitely under the control of a decreasing sequence linked with the gradient stepsizes. We then compare this new approach and assumptions with classical ones in the stochastic approximation literature. As an application of this general setting, we show how the algorithm to solve infinite dimensional stochastic optimization problems recently developped by the authors in another paper is a special case of the following perturbed gradient with stochastic noises.
Type de document :
Article dans une revue
Optimization Online, 2005
Liste complète des métadonnées

https://hal-ensta.archives-ouvertes.fr/hal-00983332
Contributeur : Aurélien Arnoux <>
Soumis le : vendredi 25 avril 2014 - 10:43:43
Dernière modification le : mercredi 6 décembre 2017 - 16:46:01

Identifiants

  • HAL Id : hal-00983332, version 1

Collections

Citation

Kengy Barty, Jean-Sébastien Roy, Cyrille Strugarek. A Perturbed Gradient Algorithm in Hilbert Spaces. Optimization Online, 2005. 〈hal-00983332〉

Partager

Métriques

Consultations de la notice

112