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Quantized Zeroth-Order Gradient Tracking Algorithm for Distributed Nonconvex Optimization Under Polyak-Łojasiewicz

Lei Xu, Xinlei Yi, Chao Deng

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    Summary
    This summary is machine-generated.

    This study introduces a quantized distributed zeroth-order algorithm for distributed nonconvex optimization. The method achieves linear convergence even with limited bandwidth and unavailable gradient information.

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    Area of Science:

    • Optimization Theory
    • Distributed Systems
    • Machine Learning

    Background:

    • Distributed optimization problems involve minimizing the average of local cost functions across multiple agents.
    • Challenges include limited communication bandwidth and the unavailability of gradient information.
    • Nonconvex cost functions add complexity to finding global optimal solutions.

    Purpose of the Study:

    • To develop a novel algorithm for distributed nonconvex optimization under communication constraints.
    • To address the limitations of bandwidth constraints and unavailable gradient information.
    • To ensure convergence to a global optimal point in distributed systems.

    Main Methods:

    • Proposing a quantized distributed zeroth-order algorithm.
    • Integrating a deterministic gradient estimator, uniform quantizer, and gradient tracking.
    • Leveraging the Polyak-Łojasiewicz and smoothness conditions for convergence analysis.

    Main Results:

    • Establishing linear convergence to a global optimal point for the proposed algorithm.
    • Demonstrating maintained linear convergence at low data rates with parameter tuning.
    • Validating theoretical findings through numerical simulations.

    Conclusions:

    • The quantized distributed zeroth-order algorithm effectively handles distributed nonconvex optimization with limited communication.
    • The algorithm offers robust performance and linear convergence guarantees under practical constraints.
    • This work provides a valuable approach for optimizing complex systems with restricted information exchange.