Decentralized Inexact Proximal Gradient Method With Network-Independent Stepsizes for Convex Composite Optimization
arXiv:2302.03238 · doi:10.1109/TSP.2023.3250839
Abstract
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 O(1/k) convergence rate of the proposed algorithm, which can be improved to o(1/k) 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.
References in corpus (9)
- On the Linear Convergence of the ADMM in Decentralized Consensus Optimization
- Harnessing Smoothness to Accelerate Distributed Optimization
- The solution path of the generalized lasso
- Multi-Agent Distributed Optimization via Inexact Consensus ADMM
- A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates
- Distributed Algorithms for Composite Optimization: Unified Framework and Convergence Analysis
- Distributed Discrete-time Optimization in Multi-agent Networks Using only Sign of Relative State
- Decomposing Linearly Constrained Nonconvex Problems by a Proximal Primal Dual Approach: Algorithms, Convergence, and Applications
- On construction of splitting contraction algorithms in a prediction-correction framework for separable convex optimization