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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-15 DOI:10.1007/s10898-024-01365-5

Zehao Xiao, Liwei Zhang

引用次数: 0

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 \(\mathcal {O}(\sqrt{N})\) objective regret and \(\mathcal {O}(\sqrt{N})\) 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.

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用于在线复合优化的在线主要半近似 ADMM 的遗憾分析

针对各类在线线性约束复合优化问题，提出了一种在线大化半近似交替方向乘法（Online-mspADMM）。该方法采用大化技术来生成易于求解的子问题。在温和的假设条件下，我们在第 N 轮建立了 \(\mathcal {O}(\sqrt{N})\) 目标遗憾和 \(\mathcal {O}(\sqrt{N})\) 约束违反遗憾。在合成数据集上的数值结果验证了关于遗憾的理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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