Bregman Proximal Method for Efficient Communications under Similarity

Fuente: arXiv
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Hauptverfasser: Beznosikov, Aleksandr, Dvinskikh, Darina, Bylinkin, Dmitry, Semenov, Andrei, Gasnikov, Alexander
Format: Preprint
Veröffentlicht: 2023
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author Beznosikov, Aleksandr
Dvinskikh, Darina
Bylinkin, Dmitry
Semenov, Andrei
Gasnikov, Alexander
author_facet Beznosikov, Aleksandr
Dvinskikh, Darina
Bylinkin, Dmitry
Semenov, Andrei
Gasnikov, Alexander
contents We propose a novel stochastic distributed method for both monotone and strongly monotone variational inequalities with Lipschitz operator and proper convex regularizers arising in various applications from game theory to adversarial training. By exploiting similarity, our algorithm overcomes the communication bottleneck that is a major issue in distributed optimization. The proposed method enjoys optimal communication complexity. All the existing distributed algorithms achieving the lower bounds under similarity condition essentially utilize the Euclidean setup. In contrast to them, our method is built upon the Bregman proximal maps and it is compatible with an arbitrary problem geometry. Thereby the proposed method fills an existing gap in this area of research. Our theoretical results are confirmed by numerical experiments on a stochastic matrix game.
format Preprint
id arxiv_https___arxiv_org_abs_2311_06953
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Bregman Proximal Method for Efficient Communications under Similarity
Beznosikov, Aleksandr
Dvinskikh, Darina
Bylinkin, Dmitry
Semenov, Andrei
Gasnikov, Alexander
Optimization and Control
We propose a novel stochastic distributed method for both monotone and strongly monotone variational inequalities with Lipschitz operator and proper convex regularizers arising in various applications from game theory to adversarial training. By exploiting similarity, our algorithm overcomes the communication bottleneck that is a major issue in distributed optimization. The proposed method enjoys optimal communication complexity. All the existing distributed algorithms achieving the lower bounds under similarity condition essentially utilize the Euclidean setup. In contrast to them, our method is built upon the Bregman proximal maps and it is compatible with an arbitrary problem geometry. Thereby the proposed method fills an existing gap in this area of research. Our theoretical results are confirmed by numerical experiments on a stochastic matrix game.
title Bregman Proximal Method for Efficient Communications under Similarity
topic Optimization and Control
url https://arxiv.org/abs/2311.06953