Accelerating Unbalanced Optimal Transport Problem Using Dynamic Penalty Updating

With the increasing applications of Optimal Transport (OT) in the machine learning field, the Unbalanced Optimal Transport (UOT) problem, as a variant of the OT problem, has gained attention for its improved generality. There is an urgent need for fast algorithms that can efficiently handle large pe...

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Veröffentlicht in:Proceedings of ... International Joint Conference on Neural Networks S. 1 - 6
Hauptverfasser: Su, Xun, Kasai, Hiroyuki
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 30.06.2024
Schlagworte:
Accuracy
Bregman Proximal Descent
Brightness
Degradation
Heuristic algorithms
Machine learning algorithms
Majorization-Maximization Algorithm
Mirror Descent
Navigation
Neural networks
Optimal Transport
Optimization
Unbalanced Optimal Transport
ISSN:2161-4407
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Abstract With the increasing applications of Optimal Transport (OT) in the machine learning field, the Unbalanced Optimal Transport (UOT) problem, as a variant of the OT problem, has gained attention for its improved generality. There is an urgent need for fast algorithms that can efficiently handle large penalty parameters. In this paper, we prove that the recently proposed Majorize-Minimization algorithm for the UOT problem can be viewed as a form of the Bregman Proximal Descent (BPD), and we propose to use the dynamic penalty updating to overcome the substantial degradation of its convergence rate in response to large penalties. Using the dynamic scheme and Nesterov acceleration of the BPD algorithm, we can successfully compute more accurate and sparser solutions for the large penalty parameter and approach the computational speed of the well-known Sinkhorn's algorithm, which sacrifices accuracy by adding an entropy item.
AbstractList With the increasing applications of Optimal Transport (OT) in the machine learning field, the Unbalanced Optimal Transport (UOT) problem, as a variant of the OT problem, has gained attention for its improved generality. There is an urgent need for fast algorithms that can efficiently handle large penalty parameters. In this paper, we prove that the recently proposed Majorize-Minimization algorithm for the UOT problem can be viewed as a form of the Bregman Proximal Descent (BPD), and we propose to use the dynamic penalty updating to overcome the substantial degradation of its convergence rate in response to large penalties. Using the dynamic scheme and Nesterov acceleration of the BPD algorithm, we can successfully compute more accurate and sparser solutions for the large penalty parameter and approach the computational speed of the well-known Sinkhorn's algorithm, which sacrifices accuracy by adding an entropy item.
Author Kasai, Hiroyuki
Su, Xun
Author_xml – sequence: 1
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  surname: Su
  fullname: Su, Xun
  organization: Waseda University,Graduate School of Fundamental Science and Engineering,Department of Communication and Computer Engineering
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  givenname: Hiroyuki
  surname: Kasai
  fullname: Kasai, Hiroyuki
  organization: Waseda University,Graduate School of Fundamental Science and Engineering,Department of Communication and Computer Engineering
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Snippet With the increasing applications of Optimal Transport (OT) in the machine learning field, the Unbalanced Optimal Transport (UOT) problem, as a variant of the...
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SubjectTerms Accuracy
Bregman Proximal Descent
Brightness
Degradation
Heuristic algorithms
Machine learning algorithms
Majorization-Maximization Algorithm
Mirror Descent
Navigation
Neural networks
Optimal Transport
Optimization
Unbalanced Optimal Transport
Title Accelerating Unbalanced Optimal Transport Problem Using Dynamic Penalty Updating
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