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Geometric Convergence of Gradient Play Algorithms for Distributed Nash Equilibrium Seeking

Tatarenko, Tatiana ; Shi, Wei ; Nedich, Angelia (2025)
Geometric Convergence of Gradient Play Algorithms for Distributed Nash Equilibrium Seeking.
In: IEEE Transactions on Automatic Control, 2021, 66 (11)
doi: 10.26083/tuprints-00017863
Article, Secondary publication, Postprint

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Item Type: Article
Type of entry: Secondary publication
Title: Geometric Convergence of Gradient Play Algorithms for Distributed Nash Equilibrium Seeking
Language: English
Date: 22 January 2025
Place of Publication: Darmstadt
Year of primary publication: 2021
Place of primary publication: New York, NY
Publisher: IEEE
Journal or Publication Title: IEEE Transactions on Automatic Control
Volume of the journal: 66
Issue Number: 11
Collation: 12 Seiten
DOI: 10.26083/tuprints-00017863
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Origin: Secondary publication service
Abstract:

We study distributed algorithms for seeking a Nash equilibrium in a class of convex networked Nash games with strongly monotone mappings. Each player has access to her own smooth local cost function and can communicate to her neighbors in some undirected graph. To deal with fast distributed learning of Nash equilibria under such settings, we introduce a so called augmented game mapping and provide conditions under which this mapping is strongly monotone. We consider a distributed gradient play algorithm for determining a Nash equilibrium (GRANE). The algorithm involves every player performing a gradient step to minimize her own cost function while sharing and retrieving information locally among her neighbors in the network. Using the reformulation of the Nash equilibrium problem based on the strong monotone augmented game mapping, we prove the convergence of this algorithm to a Nash equilibrium with a geometric rate. Further, we introduce the Nesterov type acceleration for the gradient play algorithm. We demonstrate that, similarly to the accelerated algorithms in centralized optimization and variational inequality problems, our accelerated algorithm outperforms GRANE in the convergence rate. Moreover, to relax assumptions required to guarantee the strongly monotone augmented mapping, we analyze the restricted strongly monotone property of this mapping and prove geometric convergence of the distributed gradient play under milder assumptions

Status: Postprint
URN: urn:nbn:de:tuda-tuprints-178635
Classification DDC: 500 Science and mathematics > 510 Mathematics
Date Deposited: 22 Jan 2025 10:20
Last Modified: 22 Jan 2025 10:20
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/17863
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