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arXiv 2009.02709stat.MLcs.LGmath.OCstat.CO
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有效集识别的筛选规则及其复杂性

Screening Rules and its Complexity for Active Set Identification

Riken AIP(理化学研究所革新智能综合研究中心);LTCI, Télécom Paris, Institut Polytechnique de Paris(巴黎电信学院,巴黎综合理工学院)

Eugene Ndiaye, Olivier Fercoq, Joseph Salmon

摘要:

筛选规则最近被引入作为一种技术,用于显式地识别活跃的结构,如稀疏性,在机器学习中出现的优化问题。这导致了基于大幅降维的新加速方法。我们表明,筛选规则源于次微分集和最优性条件的自然属性的组合,因此可以以一种统一的方式理解。在温和的假设下,我们分析了确定任何收敛算法的最佳活动集所需的迭代次数。我们证明了它只依赖于它的收敛速度。

英文摘要:

Screening rules were recently introduced as a technique for explicitly identifying active structures such as sparsity, in optimization problem arising in machine learning. This has led to new methods of acceleration based on a substantial dimension reduction. We show that screening rules stem from a combination of natural properties of subdifferential sets and optimality conditions, and can hence be understood in a unified way. Under mild assumptions, we analyze the number of iterations needed to identify the optimal active set for any converging algorithm. We show that it only depends on its convergence rate.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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