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Tight Linear Convergence Rate of ADMM for Decentralized Optimization
Optimization and Control · Submitted 24 May 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This paper fills the gap by incorporating both node and edge information and provides a novel convergence rate bound for decentralized ADMM that explicitly depends on network topology.
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The abstract, sentence by sentence
The present paper considers leveraging network topology information to improve the convergence rate of ADMM for decentralized optimization, where networked nodes work collaboratively to minimize the objective. Such problems can be solved efficiently using ADMM via decomposing the objective into easier subproblems. Properly exploiting network topology can significantly improve the algorithm performance. Hybrid ADMM explores the direction of exploiting node information by taking into account node centrality but fails to utilize edge information. This paper fills the gap by incorporating both node and edge information and provides a novel convergence rate bound for decentralized ADMM that explicitly depends on network topology. Such a novel bound is attainable for certain class of problems, thus tight. The explicit dependence further suggests possible directions to optimal design of edge weights to achieve the best performance. Numerical experiments show that simple heuristic methods could achieve better performance, and also exhibits robustness to topology changes.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The present paper considers leveraging network topology information to improve the convergence rate of ADMM for decentralized optimization, where networked nodes work collaboratively to minimize the objective. | background 0.53 | 0.40 | 0.05 | asserted 0.75 |
| s1 | Such problems can be solved efficiently using ADMM via decomposing the objective into easier subproblems. | background 0.99 | 0.06 | 0.02 | asserted 0.92 |
| s2 | Properly exploiting network topology can significantly improve the algorithm performance. | background 1.00 | 0.12 | 0.07 | asserted 0.90 |
| s3 | Hybrid ADMM explores the direction of exploiting node information by taking into account node centrality but fails to utilize edge information. | gap 0.64 | 0.08 | 0.04 | asserted 1.00 |
| s4 | This paper fills the gap by incorporating both node and edge information and provides a novel convergence rate bound for decentralized ADMM that explicitly depends on network topology. | contribution 1.00 | 0.94 | 0.56 | asserted 1.00 |
| s5 | Such a novel bound is attainable for certain class of problems, thus tight. | result 0.54 | 0.78 | 0.23 | asserted 0.79 |
| s6 | The explicit dependence further suggests possible directions to optimal design of edge weights to achieve the best performance. | interpretation 0.96 | 0.49 | 0.11 | hedged possibility 0.99 |
| s7 | Numerical experiments show that simple heuristic methods could achieve better performance, and also exhibits robustness to topology changes. | result 1.00 | 0.90 | 0.10 | hedged possibility 0.57 |
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Original abstract
The present paper considers leveraging network topology information to improve the convergence rate of ADMM for decentralized optimization, where networked nodes work collaboratively to minimize the objective. Such problems can be solved efficiently using ADMM via decomposing the objective into easier subproblems. Properly exploiting network topology can significantly improve the algorithm performance. Hybrid ADMM explores the direction of exploiting node information by taking into account node centrality but fails to utilize edge information. This paper fills the gap by incorporating both node and edge information and provides a novel convergence rate bound for decentralized ADMM that explicitly depends on network topology. Such a novel bound is attainable for certain class of problems, thus tight. The explicit dependence further suggests possible directions to optimal design of edge weights to achieve the best performance. Numerical experiments show that simple heuristic methods could achieve better performance, and also exhibits robustness to topology changes.
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The relation between convergence rate of ADMM and the topology of underlying graph is explored using lifted Markov chain [ref] .
How is Distributed ADMM Affected by Network Topology? · Related works · 0.88
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