Regret analysis of an online majorized semi-proximal ADMM for online composite optimization

Zehao Xiao () and Liwei Zhang ()
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Zehao Xiao: Dalian University of Technology
Liwei Zhang: Dalian University of Technology

Journal of Global Optimization, 2024, vol. 89, issue 3, No 6, 687-722

Abstract: Abstract An online majorized semi-proximal alternating direction method of multiplier (Online-mspADMM) is proposed for a broad class of online linearly constrained composite optimization problems. A majorized technique is adopted to produce subproblems which can be easily solved. Under mild assumptions, we establish $$\mathcal {O}(\sqrt{N})$$ O ( N ) objective regret and $$\mathcal {O}(\sqrt{N})$$ O ( N ) constraint violation regret at round N. We apply the Online-mspADMM to solve different types of online regularized logistic regression problems. The numerical results on synthetic data sets verify the theoretical result about regrets.

Keywords: Online majorized semi-proximal alternating direction method of multiplier; Objective regret; Constraint violation regret; Online composite optimization; Linear constraints; 90C30; 90C25; 65K05; 62J12 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-024-01365-5

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