A generalized Frank–Wolfe method with “dual averaging” for strongly convex composite optimization
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11590_2022_Article_1951.pdf
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2.14 MB
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Author(s)
Zhao, Renbo
Zhu, Qiuyun
Date Issued
November 7, 2022
Publisher
Springer Berlin Heidelberg
Citation
Zhao, Renbo and Zhu, Qiuyun. 2022. "A generalized Frank–Wolfe method with “dual averaging” for strongly convex composite optimization."
Version
Final published version
Abstract
Abstract
We propose a simple variant of the generalized Frank–Wolfe method for solving strongly convex composite optimization problems, by introducing an additional averaging step on the dual variables. We show that in this variant, one can choose a simple constant step-size and obtain a linear convergence rate on the duality gaps. By leveraging the convergence analysis of this variant, we then analyze the local convergence rate of the logistic fictitious play algorithm, which is well-established in game theory but lacks any form of convergence rate guarantees. We show that, with high probability, this algorithm converges locally at rate O(1/t), in terms of certain expected duality gap.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s11590-022-01951-0
