TY - JOUR
T1 - Graph Simplification-Aided ADMM for Decentralized Composite Optimization
AU - Wang, Bin
AU - Fang, Jun
AU - Duan, Huiping
AU - Li, Hongbin
N1 - Publisher Copyright:
© 2013 IEEE.
PY - 2021/10/1
Y1 - 2021/10/1
N2 - 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.
AB - 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.
KW - Alternating direction method of multiplier (ADMM)
KW - decentralized composite optimization
KW - graph simplification
KW - simplest bipartite graph
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U2 - 10.1109/TCYB.2019.2953538
DO - 10.1109/TCYB.2019.2953538
M3 - Article
C2 - 31831456
AN - SCOPUS:85117384234
SN - 2168-2267
VL - 51
SP - 5170
EP - 5183
JO - IEEE Transactions on Cybernetics
JF - IEEE Transactions on Cybernetics
IS - 10
ER -