Markov chain block coordinate descent

Tao Sun (), Yuejiao Sun (), Yangyang Xu () and Wotao Yin ()
Additional contact information
Tao Sun: National University of Defense Technology
Yuejiao Sun: University of California
Yangyang Xu: Rensselaer Polytechnic Institute
Wotao Yin: University of California

Computational Optimization and Applications, 2020, vol. 75, issue 1, No 2, 35-61

Abstract: Abstract The method of block coordinate gradient descent (BCD) has been a powerful method for large-scale optimization. This paper considers the BCD method that successively updates a series of blocks selected according to a Markov chain. This kind of block selection is neither i.i.d. random nor cyclic. On the other hand, it is a natural choice for some applications in distributed optimization and Markov decision process, where i.i.d. random and cyclic selections are either infeasible or very expensive. By applying mixing-time properties of a Markov chain, we prove convergence of Markov chain BCD for minimizing Lipschitz differentiable functions, which can be nonconvex. When the functions are convex and strongly convex, we establish both sublinear and linear convergence rates, respectively. We also present a method of Markov chain inertial BCD. Finally, we discuss potential applications.

Keywords: Block coordinate gradient descent; Markov chain; Markov chain Monte Carlo; Markov decision process; Decentralized optimization; Primary 90C26; Secondary 90C40; 68W15 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-019-00140-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:75:y:2020:i:1:d:10.1007_s10589-019-00140-7

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-019-00140-7

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().