Screening Rules and its Complexity for Active Set Identification

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...

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Bibliographic Details
Main Authors Ndiaye, Eugene, Fercoq, Olivier, Salmon, Joseph
Format Journal Article
LanguageEnglish
Published 2021
Subjects
Computer Science - Learning
Mathematics - Optimization and Control
Statistics - Computation
Statistics - Machine Learning
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Summary: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.
DOI:10.48550/arxiv.2009.02709