Graph Simplification-Aided ADMM for Decentralized Composite Optimization

In this article, we consider the problem of decentralized composite optimization over a connected and symmetric graph, in which each node holds its own agent-specific private convex functions, and communications are only allowed between nodes with direct links. A variety of algorithms has been propo...

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Vydáno v:IEEE transactions on cybernetics Ročník 51; číslo 10; s. 5170 - 5183
Hlavní autoři: Wang, Bin, Fang, Jun, Duan, Huiping, Li, Hongbin
Médium: Journal Article
Jazyk:angličtina
Vydáno: Piscataway IEEE 01.10.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Alternating direction method of multiplier (ADMM)
Bipartite graph
Convergence
Convex functions
decentralized composite optimization
graph simplification
Graph theory
Graphs
Lagrangian function
Laplace equations
Linear programming
Message passing
Optimization
Robot sensing systems
simplest bipartite graph
ISSN:2168-2267, 2168-2275, 2168-2275
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Shrnutí:In this article, we consider the problem of decentralized composite optimization over a connected and symmetric graph, in which each node holds its own agent-specific private convex functions, and communications are only allowed between nodes with direct links. A variety of algorithms has been proposed to solve such a problem in an alternating direction method of multiplier (ADMM) framework. Many of these algorithms, however, need to include some extra proximal term in the augmented Lagrangian function such that the resulting algorithm can be implemented in a decentralized manner. The use of the extra proximal term slows down the convergence speed because it forces the current solution to stay close to the solution obtained in the previous iteration. To address this issue, in this article, we first introduce the notion of simplest bipartite graph, which is defined as a bipartite graph that has a minimum number of edges to keep the graph connected. A simple two-step message passing-based procedure is proposed to find a simplest bipartite graph associated with the original graph. We show that the simplest bipartite graph has some interesting properties. By utilizing these properties, an ADMM without involving extra proximal terms can be developed to perform decentralized composite optimization over the simplest bipartite graph. The simulation results show that our proposed method achieves a much faster convergence speed than the existing state-of-the-art decentralized algorithms.
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2019.2953538