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Coordinate-Descent Adaptation over Hamiltonian Multi-Agent Networks.

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A new coordinate-descent incremental least-mean-square (CD-ILMS) algorithm offers faster convergence for distributed adaptation in Hamiltonian networks. It achieves similar steady-state error performance to the original ILMS algorithm, even with partial data availability.

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Area of Science:

  • Signal processing
  • Distributed systems
  • Machine learning

Background:

  • The incremental least-mean-square (ILMS) algorithm facilitates distributed adaptation in Hamiltonian networks.
  • ILMS requires complete data exchange between nodes for updating local estimates.
  • Practical limitations can hinder perfect data exchange among network nodes.

Purpose of the Study:

  • To develop a novel version of the ILMS algorithm that accommodates incomplete data exchange.
  • To analyze the convergence rate and computational complexity of the new algorithm.
  • To compare the performance of the proposed algorithm against the standard ILMS algorithm.

Main Methods:

  • Introduction of the coordinate-descent incremental LMS (CD-ILMS) algorithm, utilizing a random subset of update vector coordinates.
  • Derivation of closed-form expressions for learning curves (excess mean-square-error and mean-square deviation) using energy conservation.
  • Comparative analysis of CD-ILMS and ILMS algorithms regarding convergence and complexity.

Main Results:

  • The CD-ILMS algorithm demonstrates a faster convergence rate compared to the ILMS algorithm.
  • Both CD-ILMS and ILMS algorithms exhibit equivalent steady-state error performance.
  • Theoretical analysis using energy conservation provides accurate predictions of learning curves.

Conclusions:

  • The CD-ILMS algorithm is an efficient alternative to ILMS for distributed adaptation when data exchange is imperfect.
  • CD-ILMS offers improved convergence speed without compromising steady-state accuracy.
  • Numerical simulations validate the theoretical findings and the practical efficiency of CD-ILMS.