A new class of composite objective multistep estimating sequence techniques

Endrit Dosti, Sergiy A. Vorobyov*, Themistoklis Charalambous

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

A plethora of problems arising in signal processing, machine learning and statistics can be cast as large-scale optimization problems with a composite objective structure. Such problems are typically solved by utilizing iterative first-order algorithms. In this work, we devise a new accelerated gradient-based estimating sequence technique for solving large-scale optimization problems with composite objective structure. Specifically, we introduce a new class of estimating functions, which are obtained by utilizing both a tight lower bound on the objective function, as well as the gradient mapping technique. Then, using the proposed estimating functions, we construct a class of Composite Objective Multi-step Estimating-sequence Techniques (COMET), which are endowed with an efficient line-search procedure. We prove that our proposed COMET enjoys the accelerated convergence rate, and our newly established convergence results allow for step-size adaptation. Our theoretical findings are supported by extensive computational experiments on various problem types and real-world datasets. Moreover, our numerical results show evidence of the robustness of the proposed method to the imperfect knowledge of the smoothness and strong convexity parameters.

Original languageEnglish
Article number108889
Number of pages14
JournalSignal Processing
Volume206
Early online date16 Dec 2022
DOIs
Publication statusPublished - May 2023
MoE publication typeA1 Journal article-refereed

Keywords

  • Accelerated first-order methods
  • Composite objective
  • Estimating sequence
  • Gradient mapping
  • Large-scale optimization
  • Line-search

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