Accelerated Gradient Play Algorithm for Distributed Nash Equilibrium Seeking

Tatiana Tatarenko, Wei Shi, Angelia Nedich

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study distributed algorithms for seeking a Nash equilibrium in a class of non-cooperative 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. We first consider a distributed gradient play algorithm, which we call GRANE, for determining a Nash equilibrium. 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. 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.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3561-3566
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Nash Equilibrium
Gradient
Cost functions
Cost Function
Strongly Monotone Mapping
Non-cooperative Game
Variational Inequality Problem
Distributed Algorithms
Parallel algorithms
Undirected Graph
Convergence Rate
Sharing
Minimise
Optimization
Demonstrate

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Tatarenko, T., Shi, W., & Nedich, A. (2019). Accelerated Gradient Play Algorithm for Distributed Nash Equilibrium Seeking. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 3561-3566). [8619479] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619479

Accelerated Gradient Play Algorithm for Distributed Nash Equilibrium Seeking. / Tatarenko, Tatiana; Shi, Wei; Nedich, Angelia.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 3561-3566 8619479 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Tatarenko, T, Shi, W & Nedich, A 2019, Accelerated Gradient Play Algorithm for Distributed Nash Equilibrium Seeking. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619479, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 3561-3566, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8619479
Tatarenko T, Shi W, Nedich A. Accelerated Gradient Play Algorithm for Distributed Nash Equilibrium Seeking. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 3561-3566. 8619479. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8619479
Tatarenko, Tatiana ; Shi, Wei ; Nedich, Angelia. / Accelerated Gradient Play Algorithm for Distributed Nash Equilibrium Seeking. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 3561-3566 (Proceedings of the IEEE Conference on Decision and Control).
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