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

  • Ehsan Nekouei
  • Tansu Alpcan
  • Robin J. Evans
Chapter
Part of the Systems & Control: Foundations & Applications book series (SCFA)

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.

Notes

Acknowledgements

The authors would like to thank Prof. Girish Nair from The University of Melbourne for his contributions and fruitful discussions. This work was supported by the Australian Research Councils Discovery Projects funding scheme (DP140100819).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.KTH Royal Institute of TechnologystockholmSweden
  2. 2.The University of MelbourneParkville, MelbourneAustralia

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