Impact of Quantized Inter-agent Communications on Game-Theoretic and distributed Optimization Algorithms

Research output: Chapters, Conference Papers, Creative and Literary Works (RGC: 12, 32, 41, 45)12_Chapter in an edited book (Author)peer-review

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Author(s)

Detail(s)

Original languageEnglish
Title of host publicationUncertainty in Complex Networked Systems
Subtitle of host publicationIn Honor of Roberto Tempo
EditorsTamer Başar
PublisherBirkhauser
Pages501-532
Publication statusPublished - 2018
Externally publishedYes

Publication series

NameSystems and Control: Foundations and Applications
ISSN (Print)2324-9749
ISSN (Electronic)2324-9757

Abstract

Quantized inter-agent communications in game-theoretic and distributed optimization algorithms generate uncertainty that affects the asymptotic and transient behavior of such algorithms. This chapter uses the information-theoretic notion of differential entropy power to establish universal bounds on the maximum exponential convergence rates of primal-dual and gradient-based Nash seeking algorithms under quantized communications. These bounds depend on the inter-agent data rate and the local behavior of the agents’ objective functions, and are independent of the quantizer structure. The presented results provide trade-offs between the speed of exponential convergence, the agents’ objective functions, the communication bit rates, and the number of agents and constraints. For the proposed Nash seeking algorithm, the transient performance is studied and an upper bound on the average time required to settle inside a specified ball around the Nash equilibrium is derived under uniform quantization. Furthermore, an upper bound on the probability that the agents’ actions lie outside this ball is established. This bound decays double exponentially with time.

Citation Format(s)

Impact of Quantized Inter-agent Communications on Game-Theoretic and distributed Optimization Algorithms. / Nekouei, Ehsan; Alpcan, Tansu; Evans, Robin J.

Uncertainty in Complex Networked Systems: In Honor of Roberto Tempo. ed. / Tamer Başar. Birkhauser, 2018. p. 501-532 (Systems and Control: Foundations and Applications).

Research output: Chapters, Conference Papers, Creative and Literary Works (RGC: 12, 32, 41, 45)12_Chapter in an edited book (Author)peer-review