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

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  • Zehao Xiao

    (Dalian University of Technology)

  • Liwei Zhang

    (Dalian University of Technology)

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.

Suggested Citation

  • Zehao Xiao & Liwei Zhang, 2024. "Regret analysis of an online majorized semi-proximal ADMM for online composite optimization," Journal of Global Optimization, Springer, vol. 89(3), pages 687-722, July.
    • Handle: RePEc:spr:jglopt:v:89:y:2024:i:3:d:10.1007_s10898-024-01365-5
    DOI: 10.1007/s10898-024-01365-5
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    References listed on IDEAS

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    1. Deren Han & Defeng Sun & Liwei Zhang, 2018. "Linear Rate Convergence of the Alternating Direction Method of Multipliers for Convex Composite Programming," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 622-637, May.
    2. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
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