Restarting the accelerated coordinate descent method with a rough strong convexity estimate

Olivier Fercoq () and Zheng Qu ()
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Olivier Fercoq: Université Paris-Saclay
Zheng Qu: The University of Hong Kong

Computational Optimization and Applications, 2020, vol. 75, issue 1, No 3, 63-91

Abstract: Abstract We propose new restarting strategies for the accelerated coordinate descent method. Our main contribution is to show that for a well chosen sequence of restarting times, the restarted method has a nearly geometric rate of convergence. A major feature of the method is that it can take profit of the local quadratic error bound of the objective function without knowing the actual value of the error bound. We also show that under the more restrictive assumption that the objective function is strongly convex, any fixed restart period leads to a geometric rate of convergence. Finally, we illustrate the properties of the algorithm on a regularized logistic regression problem and on a Lasso problem.

Keywords: Accelerated coordinate descent; Restarting strategies; Unknown strong convexity; Local quadratic error bound (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-019-00137-2

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