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MUSIC: Accelerated Convergence for Distributed Optimization With Inexact and Exact Methods.

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    This study introduces the Multi-Updates Single-Combination (MUSIC) framework to accelerate distributed optimization. MUSIC enables faster convergence in networked systems by allowing multiple local updates per agent per iteration.

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    Area of Science:

    • Distributed optimization
    • Networked systems
    • Machine learning

    Background:

    • Gradient-type distributed optimization is crucial for networked agent systems.
    • Current methods with single updates per iteration limit convergence speed.

    Purpose of the Study:

    • To propose an accelerated framework, MUSIC, for distributed optimization.
    • To develop new algorithms with enhanced convergence and communication efficiency.

    Main Methods:

    • Introducing the Multi-Updates Single-Combination (MUSIC) framework.
    • Integrating inexact and exact distributed optimization methods into MUSIC.
    • Developing rigorous convergence analysis to identify and resolve steady-state errors.

    Main Results:

    • Two new algorithms exhibiting accelerated linear convergence and high communication efficiency.
    • Identification of steady-state error sources in inexact distributed optimization.
    • Validation of theoretical analysis and performance advantages through numerical results.

    Conclusions:

    • The MUSIC framework significantly accelerates distributed optimization in networked systems.
    • The developed algorithms offer a balance of speed and communication efficiency.
    • The study provides insights into managing errors in inexact distributed optimization.