On linear convergence of two decentralized algorithms
arXiv:1906.07225
Abstract
Decentralized algorithms solve multi-agent problems over a connected network, where the information can only be exchanged with the accessible neighbors. Though there exist several decentralized optimization algorithms, there are still gaps in convergence conditions and rates between decentralized and centralized algorithms. In this paper, we fill some gaps by considering two decentralized algorithms: EXTRA and NIDS. They both converge linearly with strongly convex objective functions. We will answer two questions regarding them. What are the optimal upper bounds for their stepsizes? Do decentralized algorithms require more properties on the functions for linear convergence than centralized ones? More specifically, we relax the required conditions for linear convergence of both algorithms. For EXTRA, we show that the stepsize is comparable to that of centralized algorithms. For NIDS, the upper bound of the stepsize is shown to be exactly the same as the centralized ones. In addition, we relax the requirement for the objective functions and the mixing matrices. We provide the linear convergence results for both algorithms under the weakest conditions.
arXiv commentaccepted to JOTA
References in corpus (7)
- On the Linear Convergence of the ADMM in Decentralized Consensus Optimization
- Multi-Agent Distributed Optimization via Inexact Consensus ADMM
- A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates
- Optimal algorithms for smooth and strongly convex distributed optimization in networks
- ExtraPush for convex smooth decentralized optimization over directed networks
- A Linearly Convergent Proximal Gradient Algorithm for Decentralized Optimization
- On the Linear Convergence of Distributed Optimization over Directed Graphs