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Decentralized Online Optimization With Compressed Communication Over Directed Graphs.

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    This study introduces a compressed communication algorithm for decentralized online optimization in multiagent systems. The novel approach achieves a sublinear regret bound for strongly convex functions, improving efficiency in large networks.

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    Area of Science:

    • Control Theory
    • Distributed Optimization
    • Networked Systems

    Background:

    • Decentralized online optimization problems are crucial for multiagent systems.
    • Communication bottlenecks hinder performance in large-scale, high-dimensional networks.

    Purpose of the Study:

    • To design a decentralized online algorithm addressing communication bottlenecks.
    • To achieve efficient global loss minimization in multiagent systems with compressed communication.

    Main Methods:

    • A novel decentralized online gradient push-sum with compressed communication (CC-DOGPS) algorithm was developed.
    • The algorithm operates over strongly connected directed graphs in multiagent systems.
    • Theoretical analysis focused on strongly convex functions and time-varying local losses.

    Main Results:

    • A sublinear regret bound of O((ln T)^2) was derived for the CC-DOGPS algorithm, where T is the time horizon.
    • The algorithm effectively manages time-varying local loss functions known only to individual agents.
    • Numerical simulations validated the theoretical findings and demonstrated algorithm efficiency.

    Conclusions:

    • The proposed CC-DOGPS algorithm offers an efficient solution for decentralized online optimization under communication constraints.
    • The sublinear regret bound highlights the algorithm's scalability and effectiveness for large networks.
    • This work contributes to advancing distributed optimization techniques in complex multiagent systems.