Asynchronous Distributed Nonsmooth Composite Optimization via Computation-Efficient Primal-Dual Proximal Algorithms

This paper focuses on a distributed nonsmooth composite optimization problem over a multiagent networked system, in which each agent is equipped with a local Lipschitz-differentiable function and two possibly nonsmooth functions, one of which incorporates a linear mapping. To address this problem, w...

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Published in:	IEEE transactions on emerging topics in computational intelligence Vol. 9; no. 2; pp. 1595 - 1609
Main Authors:	Ran, Liang, Li, Huaqing, Zheng, Lifeng, Li, Jun
Format:	Journal Article
Language:	English
Published:	Piscataway IEEE 01.04.2025 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Asynchrony Convergence Convex functions delayed communication Delays Distributed algorithms distributed optimization algorithm Multiagent systems nonsmooth convex functions Operators (mathematics) Optimization Vectors
ISSN:	2471-285X, 2471-285X
Online Access:	Get full text
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Abstract	This paper focuses on a distributed nonsmooth composite optimization problem over a multiagent networked system, in which each agent is equipped with a local Lipschitz-differentiable function and two possibly nonsmooth functions, one of which incorporates a linear mapping. To address this problem, we introduce a synchronous distributed algorithm featuring uncoordinated relaxed factors. It serves as a generalized relaxed version of the recent method TriPD-Dist. Notably, the considered problem in the presence of asynchrony and delays remains relatively unexplored. In response, a new asynchronous distributed primal-dual proximal algorithm is first proposed, rooted in a comprehensive asynchronous model. It is operated under the assumption that agents utilize possibly outdated information from their neighbors, while considering arbitrary, time-varying, yet bounded delays. With some special adjustments, new asynchronous distributed extensions of existing centralized methods are obtained via the proposed asynchronous algorithm. Theoretically, a new convergence analysis technique of the proposed algorithms is provided. Specifically, a sublinear convergence rate is explicitly derived by showcasing that the iteration behaves as a nonexpansive operator. In addition, the proposed asynchronous algorithm converges the optimal solution in expectation under the same step-size conditions as its synchronous counterpart. Finally, numerical studies substantiate the efficacy of the proposed algorithms and validate their performance in practical scenarios.
AbstractList	This paper focuses on a distributed nonsmooth composite optimization problem over a multiagent networked system, in which each agent is equipped with a local Lipschitz-differentiable function and two possibly nonsmooth functions, one of which incorporates a linear mapping. To address this problem, we introduce a synchronous distributed algorithm featuring uncoordinated relaxed factors. It serves as a generalized relaxed version of the recent method TriPD-Dist. Notably, the considered problem in the presence of asynchrony and delays remains relatively unexplored. In response, a new asynchronous distributed primal-dual proximal algorithm is first proposed, rooted in a comprehensive asynchronous model. It is operated under the assumption that agents utilize possibly outdated information from their neighbors, while considering arbitrary, time-varying, yet bounded delays. With some special adjustments, new asynchronous distributed extensions of existing centralized methods are obtained via the proposed asynchronous algorithm. Theoretically, a new convergence analysis technique of the proposed algorithms is provided. Specifically, a sublinear convergence rate is explicitly derived by showcasing that the iteration behaves as a nonexpansive operator. In addition, the proposed asynchronous algorithm converges the optimal solution in expectation under the same step-size conditions as its synchronous counterpart. Finally, numerical studies substantiate the efficacy of the proposed algorithms and validate their performance in practical scenarios.
Author	Li, Jun Ran, Liang Zheng, Lifeng Li, Huaqing
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SubjectTerms	Algorithms Asynchrony Convergence Convex functions delayed communication Delays Distributed algorithms distributed optimization algorithm Multiagent systems nonsmooth convex functions Operators (mathematics) Optimization Vectors
Title	Asynchronous Distributed Nonsmooth Composite Optimization via Computation-Efficient Primal-Dual Proximal Algorithms
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