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A Fast Row-Stochastic Decentralized Method for Distributed Optimization Over Directed Graphs
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DOI：10.1109/TAC.2023.3275927.png)
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Abstract
En 中文
In this article, we introduce a fast row-stochastic decentralized algorithm, referred to as FRSD, to solve consensus optimization problems over directed communication graphs. The proposed algorithm only utilizes row-stochastic weights, leading to certain practical advantages in broadcast communication settings over those requiring column-stochastic weights. Under the assumption that each node-specific function is smooth and strongly convex, we show that the FRSD iterate sequence converges with a linear rate to the optimal consensus solution. In contrast to the existing methods for directed networks, FRSD enjoys linear convergence without employing a gradient tracking (GT) technique explicitly, rather it implements GT implicitly with the use of a novel momentum term, which leads to a significant reduction in communication and storage overhead for each node when FRSD is implemented for solving high-dimensional problems over small-to-medium scale networks. In the numerical tests, we compare FRSD with other state-of-the-art methods, which use row-stochastic and/or column-stochastic weights.
Keywords:
Optimization
Convergence
Convex functions
Directed graphs
Communication networks
Complexity theory
Topology
Consensus
directed graphs
distributed optimization
linear convergence
row-stochastic weights
Journal
IF:
7
Papers:
1.3W
Citations:
6.7W