BLOCK-COORDINATE FRANK-WOLFE ALGORITHM AND CONVERGENCE ANALYSIS FOR SEMI-RELAXED OPTIMAL TRANSPORT PROBLEM

Takumi Fukunaga, Hiroyuki Kasai*

*この研究の対応する著者

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

The optimal transport (OT) problem has been used widely for machine learning. It is necessary for computation of an OT problem to solve linear programming with tight mass-conservation constraints. These constraints prevent its application to large-scale problems. To address this issue, loosening such constraints enables us to propose the relaxed-OT method using a faster algorithm. This approach has demonstrated its effectiveness for applications. However, it remains slow. As a superior alternative, we propose a fast block-coordinate Frank-Wolfe (BCFW) algorithm for a convex semi-relaxed OT. Specifically, we prove their upper bounds of the worst convergence iterations, and equivalence between the linearization duality gap and the Lagrangian duality gap. Additionally, we develop two fast variants of the proposed BCFW. Numerical experiments have demonstrated that our proposed algorithms are effective for color transfer and surpass state-of-the-art algorithms. This report presents a short version of [1]. The source code is available at https://github.com/hiroyuki-kasai/srot.

本文言語English
ホスト出版物のタイトル2022 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Proceedings
出版社Institute of Electrical and Electronics Engineers Inc.
ページ5433-5437
ページ数5
ISBN(電子版)9781665405409
DOI
出版ステータスPublished - 2022
イベント47th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Virtual, Online, Singapore
継続期間: 2022 5月 232022 5月 27

出版物シリーズ

名前ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
2022-May
ISSN(印刷版)1520-6149

Conference

Conference47th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022
国/地域Singapore
CityVirtual, Online
Period22/5/2322/5/27

ASJC Scopus subject areas

  • ソフトウェア
  • 信号処理
  • 電子工学および電気工学

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