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Distributed Gradient Tracking Methods with Finite Data Rates

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Abstract

This paper studies the distributed optimization problem over an undirected connected graph subject to digital communications with a finite data rate, where each agent holds a strongly convex and smooth cost function. The agents need to cooperatively minimize the average of all agents’ cost functions. Each agent builds an encoder/decoder pair that produces transmitted messages to its neighbors with a finite-level uniform quantizer, and recovers its neighbors’ states by a recursive decoder with received quantized signals. Combining the adaptive encoder/decoder scheme with the gradient tracking method, the authors propose a distributed quantized algorithm. The authors prove that the optimization can be achieved at a linear rate, even when agents communicate at 1-bit data rate. Numerical examples are also conducted to illustrate theoretical results.

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Authors and Affiliations

  1. Department of Control Science and Engineering, Tongji University, Shanghai, 200082, China

    Xiaoyu Ma, Peng Yi & Jie Chen

  2. Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University, Shanghai, 200082, China

    Peng Yi & Jie Chen

Authors
  1. Xiaoyu Ma
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  2. Peng Yi
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  3. Jie Chen
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Corresponding authors

Correspondence to Xiaoyu Ma, Peng Yi or Jie Chen.

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Ma, X., Yi, P. & Chen, J. Distributed Gradient Tracking Methods with Finite Data Rates. J Syst Sci Complex 34, 1927–1952 (2021). https://doi.org/10.1007/s11424-021-1231-9

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  • DOI: https://doi.org/10.1007/s11424-021-1231-9

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