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The present paper considers leveraging network topology information toimprove the convergence rate of ADMM for decentralized optimization, wherenetworked nodes work collaboratively to minimize the objective. Such problemscan be solved efficiently using ADMM via decomposing the objective into easiersubproblems. Properly exploiting network topology can significantly improve thealgorithm performance. Hybrid ADMM explores the direction of exploiting nodeinformation by taking into account node centrality but fails to utilize edgeinformation. This paper fills the gap by incorporating both node and edgeinformation and provides a novel convergence rate bound for decentralized ADMMthat explicitly depends on network topology. Such a novel bound is attainablefor certain class of problems, thus tight. The explicit dependence furthersuggests possible directions to optimal design of edge weights to achieve thebest performance. Numerical experiments show that simple heuristic methodscould achieve better performance, and also exhibits robustness to topologychanges.

Tight Linear Convergence Rate of ADMM for Decentralized Optimization