Decentralized Inexact Proximal Gradient Method With Network-Independent Stepsizes for Convex Composite Optimization

This paper proposes a novel CTA (Combine-Then-Adapt)-based decentralized algorithm for solving convex composite optimization problems over undirected and connected networks. The local loss function in these problems contains both smooth and nonsmooth terms. The proposed algorithm uses uncoordinated...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 71; pp. 1 - 16
Main Authors: Guo, Luyao, Shi, Xinli, Cao, Jinde, Wang, Zihao
Format: Journal Article
Language:English
Published: New York IEEE 01.01.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation algorithms
Convergence
Decentralized optimization
Exact solutions
Gradient methods
inexact proximal gradient method
linear convergence
Measurement
network independent
Network topology
Optimization
Signal processing algorithms
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:This paper proposes a novel CTA (Combine-Then-Adapt)-based decentralized algorithm for solving convex composite optimization problems over undirected and connected networks. The local loss function in these problems contains both smooth and nonsmooth terms. The proposed algorithm uses uncoordinated network-independent constant stepsizes and only needs to approximately solve a sequence of proximal mappings, which is advantageous for solving decentralized composite optimization problems where the proximal mappings of the nonsmooth loss functions may not have analytical solutions. For the general convex case, we prove an <inline-formula><tex-math notation="LaTeX">O(1/k)</tex-math></inline-formula> convergence rate of the proposed algorithm, which can be improved to <inline-formula><tex-math notation="LaTeX">o(1/k)</tex-math></inline-formula> if the proximal mappings are solved exactly. Furthermore, with metric subregularity, we establish a linear convergence rate for the proposed algorithm. Numerical experiments demonstrate the efficiency of the algorithm.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2023.3250839