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

This article focuses on distributed nonconvex optimization by exchanging information between agents to minimize the average of local nonconvex cost functions. The communication channel between agents is normally constrained by limited bandwidth, and the gradient information is typically unavailable....

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Bibliographic Details
Published in:IEEE transactions on cybernetics Vol. 54; no. 10; pp. 5746 - 5758
Main Authors: Xu, Lei, Yi, Xinlei, Deng, Chao, Shi, Yang, Chai, Tianyou, Yang, Tao
Format: Journal Article
Language:English
Published: United States IEEE 01.10.2024
Subjects:
Convergence
Cost function
Deep learning
Distributed algorithms
Gradient methods
Gradient tracking algorithm
linear convergence
nonconvex optimization
Quantization (signal)
uniform quantizer
zeroth-order algorithm
ISSN:2168-2267, 2168-2275, 2168-2275
Online Access:Get full text
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Summary:This article focuses on distributed nonconvex optimization by exchanging information between agents to minimize the average of local nonconvex cost functions. The communication channel between agents is normally constrained by limited bandwidth, and the gradient information is typically unavailable. To overcome these limitations, we propose a quantized distributed zeroth-order algorithm, which integrates the deterministic gradient estimator, the standard uniform quantizer, and the distributed gradient tracking algorithm. We establish linear convergence to a global optimal point for the proposed algorithm by assuming Polyak-Łojasiewicz condition for the global cost function and smoothness condition for the local cost functions. Moreover, the proposed algorithm maintains linear convergence at low-data rates with a proper selection of algorithm parameters. Numerical simulations validate the theoretical results.
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2024.3384924