Markov Chain Lifting and Distributed ADMM

Guilherme França; José Bento

doi:10.1109/lsp.2017.2654860

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arXiv · 1703.03859

Markov Chain Lifting and Distributed ADMM

Guilherme França·José Bento

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Abstract

The time to converge to the steady state of a finite Markov chain can be greatly reduced by a lifting operation, which creates a new Markov chain on an expanded state space. For a class of quadratic objectives, we show an analogous behavior where a distributed ADMM algorithm can be seen as a lifting of Gradient Descent algorithm. This provides a deep insight for its faster convergence rate under optimal parameter tuning. We conjecture that this gain is always present, as opposed to the lifting of a Markov chain which sometimes only provides a marginal speedup.

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stat.ML cs.DS cs.IT cs.LG math.IT math.OC

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BibTeX RIS

Guilherme França, José Bento. 2017-03-10. Markov Chain Lifting and Distributed ADMM. https://doi.org/10.1109/lsp.2017.2654860

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