On the Convergence of Asynchronous Parallel Iteration with Unbounded Delays

Zhimin Peng University of California, Los Angeles Yangyang Xu Rensselaer Polytechnic Institute Ming Yan Michigan State University Wotao Yin University of California, Los Angeles

Optimization and Control mathscidoc:1903.27003

Journal of the Operations Research Society of China, 7, (1), 5-42, 2019.3
Recent years have witnessed the surge of asynchronous parallel (async-parallel) iterative algorithms due to problems involving very large-scale data and a large number of decision variables. Because of asynchrony, the iterates are computed with outdated information, and the age of the outdated information, which we call delay, is the number of times it has been updated since its creation. Almost all recent works prove convergence under the assumption of a finite maximum delay and set their stepsize parameters accordingly. However, the maximum delay is practically unknown. This paper presents convergence analysis of an async-parallel method from a probabilistic viewpoint, and it allows for large unbounded delays. An explicit formula of stepsize that guarantees convergence is given depending on delays’ statistics. With p+1 identical processors, we empirically measured that delays closely follow the Poisson distribution with parameter p, matching our theoretical model, and thus, the stepsize can be set accordingly. Simulations on both convex and nonconvex optimization problems demonstrate the validness of our analysis and also show that the existing maximum-delay-induced stepsize is too conservative, often slows down the convergence of the algorithm.
Asynchronous unbounded delays Nonconvex Convex
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@inproceedings{zhimin2019on,
  title={On the Convergence of Asynchronous Parallel Iteration with Unbounded Delays},
  author={Zhimin Peng, Yangyang Xu, Ming Yan, and Wotao Yin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190319202739791065207},
  booktitle={Journal of the Operations Research Society of China},
  volume={7},
  number={1},
  pages={5-42},
  year={2019},
}
Zhimin Peng, Yangyang Xu, Ming Yan, and Wotao Yin. On the Convergence of Asynchronous Parallel Iteration with Unbounded Delays. 2019. Vol. 7. In Journal of the Operations Research Society of China. pp.5-42. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190319202739791065207.
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