Distributed Stochastic Proximal Algorithm With Random Reshuffling for Nonsmooth Finite-Sum Optimization

The nonsmooth finite-sum minimization is a fundamental problem in machine learning. This article develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying multiagent networks. The objective function is a sum of differ...

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Veröffentlicht in:	IEEE transaction on neural networks and learning systems Jg. 35; H. 3; S. 1 - 15
Hauptverfasser:	Jiang, Xia, Zeng, Xianlin, Sun, Jian, Chen, Jie, Xie, Lihua
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	United States IEEE 01.03.2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithms Convergence Convex functions Costs Distributed optimization Machine learning Machine learning algorithms Minimization Multiagent systems Objective function Optimization proximal operator random reshuffling (RR) Regularization stochastic algorithm Stochasticity Sums time-varying graphs
ISSN:	2162-237X, 2162-2388, 2162-2388
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Abstract	The nonsmooth finite-sum minimization is a fundamental problem in machine learning. This article develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying multiagent networks. The objective function is a sum of differentiable convex functions and nonsmooth regularization. Each agent in the network updates local variables by local information exchange and cooperates to seek an optimal solution. We prove that local variable estimates generated by the proposed algorithm achieve consensus and are attracted to a neighborhood of the optimal solution with an <inline-formula> <tex-math notation="LaTeX">\mathcal{O}(({1}/{T})+({1}/{\sqrt{T}}))</tex-math> </inline-formula> convergence rate, where <inline-formula> <tex-math notation="LaTeX">T</tex-math> </inline-formula> is the total number of iterations. Finally, some comparative simulations are provided to verify the convergence performance of the proposed algorithm.
AbstractList	The nonsmooth finite-sum minimization is a fundamental problem in machine learning. This article develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying multiagent networks. The objective function is a sum of differentiable convex functions and nonsmooth regularization. Each agent in the network updates local variables by local information exchange and cooperates to seek an optimal solution. We prove that local variable estimates generated by the proposed algorithm achieve consensus and are attracted to a neighborhood of the optimal solution with an O((1/T)+(1/√T)) convergence rate, where T is the total number of iterations. Finally, some comparative simulations are provided to verify the convergence performance of the proposed algorithm.The nonsmooth finite-sum minimization is a fundamental problem in machine learning. This article develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying multiagent networks. The objective function is a sum of differentiable convex functions and nonsmooth regularization. Each agent in the network updates local variables by local information exchange and cooperates to seek an optimal solution. We prove that local variable estimates generated by the proposed algorithm achieve consensus and are attracted to a neighborhood of the optimal solution with an O((1/T)+(1/√T)) convergence rate, where T is the total number of iterations. Finally, some comparative simulations are provided to verify the convergence performance of the proposed algorithm. The nonsmooth finite-sum minimization is a fundamental problem in machine learning. This article develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying multiagent networks. The objective function is a sum of differentiable convex functions and nonsmooth regularization. Each agent in the network updates local variables by local information exchange and cooperates to seek an optimal solution. We prove that local variable estimates generated by the proposed algorithm achieve consensus and are attracted to a neighborhood of the optimal solution with an [Formula Omitted] convergence rate, where [Formula Omitted] is the total number of iterations. Finally, some comparative simulations are provided to verify the convergence performance of the proposed algorithm. The nonsmooth finite-sum minimization is a fundamental problem in machine learning. This article develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying multiagent networks. The objective function is a sum of differentiable convex functions and nonsmooth regularization. Each agent in the network updates local variables by local information exchange and cooperates to seek an optimal solution. We prove that local variable estimates generated by the proposed algorithm achieve consensus and are attracted to a neighborhood of the optimal solution with an O((1/T)+(1/√T)) convergence rate, where T is the total number of iterations. Finally, some comparative simulations are provided to verify the convergence performance of the proposed algorithm. The nonsmooth finite-sum minimization is a fundamental problem in machine learning. This article develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying multiagent networks. The objective function is a sum of differentiable convex functions and nonsmooth regularization. Each agent in the network updates local variables by local information exchange and cooperates to seek an optimal solution. We prove that local variable estimates generated by the proposed algorithm achieve consensus and are attracted to a neighborhood of the optimal solution with an <inline-formula> <tex-math notation="LaTeX">\mathcal{O}(({1}/{T})+({1}/{\sqrt{T}}))</tex-math> </inline-formula> convergence rate, where <inline-formula> <tex-math notation="LaTeX">T</tex-math> </inline-formula> is the total number of iterations. Finally, some comparative simulations are provided to verify the convergence performance of the proposed algorithm.
Author	Jiang, Xia Xie, Lihua Chen, Jie Sun, Jian Zeng, Xianlin
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SubjectTerms	Algorithms Convergence Convex functions Costs Distributed optimization Machine learning Machine learning algorithms Minimization Multiagent systems Objective function Optimization proximal operator random reshuffling (RR) Regularization stochastic algorithm Stochasticity Sums time-varying graphs
Title	Distributed Stochastic Proximal Algorithm With Random Reshuffling for Nonsmooth Finite-Sum Optimization
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