New Version of Mirror Prox for Variational Inequalities with Adaptation to Inexactness - Calcul des Variations, Géométrie, Image Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

New Version of Mirror Prox for Variational Inequalities with Adaptation to Inexactness

Résumé

Some adaptive analogue of the Mirror Prox method for variational inequalities is proposed. In this work we consider the adaptation not only to the value of the Lipschitz constant, but also to the magnitude of the oracle error. This approach, in particular, allows us to prove a complexity near $O\left(\frac{1}{\varepsilon}\log_2\frac{1}{\varepsilon}\right)$ for variational inequalities for a special class of monotone bounded operators. This estimate is optimal for variational inequalities with monotone Lipschitz-continuous operators. However, there exists some error, which may be insignificant. The results of experiments on the comparison of the proposed approach with some known analogues are presented. Also, we discuss the results of the experiments for matrix games in the case of using non-Euclidean proximal setup.
Fichier principal
Vignette du fichier
1907.13455.pdf (283.35 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02322208 , version 1 (21-10-2019)

Identifiants

Citer

Fedor Stonyakin, Evgeniya Vorontsova, Mohammad Alkousa. New Version of Mirror Prox for Variational Inequalities with Adaptation to Inexactness. 2019. ⟨hal-02322208⟩
43 Consultations
77 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More