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Distributed Constrained Optimization With Delayed Subgradient Information Over Time-Varying Network Under Adaptive

Jie Liu, Zhan Yu, Daniel W C Ho

    IEEE Transactions on Neural Networks and Learning Systems
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    Summary
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    This study introduces an adaptive quantization method for distributed optimization with delayed subgradient information over networks. The approach achieves optimal convergence rates without quantization error, enhancing distributed algorithm performance.

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    Area of Science:

    • Distributed optimization
    • Networked systems
    • Control theory

    Background:

    • Distributed constrained optimization problems are common in networked systems.
    • Delayed subgradient information and time-varying networks pose significant challenges.
    • Limited data rates in communication channels further complicate these problems.

    Purpose of the Study:

    • To propose an adaptive quantization method for distributed optimization with delayed subgradient information.
    • To develop a generalized algorithm using Bregman divergence and non-Euclidean projections.
    • To analyze the convergence properties and achieve optimal convergence rates.

    Main Methods:

    • An adaptive quantization technique is developed to handle limited data rates.
    • A mirror descent algorithm incorporating delayed subgradient information is established.
    • A non-Euclidean Bregman projection-based scheme generalizes existing distributed algorithms.

    Main Results:

    • The proposed adaptive quantization method eliminates quantization error.
    • The algorithm achieves optimal convergence rates under specific conditions.
    • Numerical examples validate the effectiveness of the developed method.

    Conclusions:

    • The adaptive quantization method is effective for distributed optimization with delayed information.
    • The generalized Bregman projection approach enhances existing distributed algorithms.
    • The study provides a robust framework for networked optimization problems.