EURASIP Journal on Advances in Signal Processing (Dec 2018)

Hybrid ADMM: a unifying and fast approach to decentralized optimization

  • Meng Ma,
  • Athanasios N. Nikolakopoulos,
  • Georgios B. Giannakis

DOI
https://doi.org/10.1186/s13634-018-0589-x
Journal volume & issue
Vol. 2018, no. 1
pp. 1 – 17

Abstract

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Abstract The present work introduces the hybrid consensus alternating direction method of multipliers (H-CADMM), a novel framework for optimization over networks which unifies existing distributed optimization approaches, including the centralized and the decentralized consensus ADMM. H-CADMM provides a flexible tool that leverages the underlying graph topology in order to achieve a desirable sweet spot between node-to-node communication overhead and rate of convergence—thereby alleviating known limitations of both C-CADMM and D-CADMM. A rigorous analysis of the novel method establishes linear convergence rate and also guides the choice of parameters to optimize this rate. The novel hybrid update rules of H-CADMM lend themselves to “in-network acceleration” that is shown to effect considerable—and essentially “free-of-charge”—performance boost over the fully decentralized ADMM. Comprehensive numerical tests validate the analysis and showcase the potential of the method in tackling efficiently, widely useful learning tasks.

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