Efficient Optimal Transport Algorithm by Accelerated Gradient Descent
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Published:2022-06-28
Issue:9
Volume:36
Page:10119-10128
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ISSN:2374-3468
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Container-title:Proceedings of the AAAI Conference on Artificial Intelligence
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language:
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Short-container-title:AAAI
Author:
An Dongsheng,Lei Na,Xu Xiaoyin,Gu Xianfeng
Abstract
Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning.
However, computing discrete optimal transport plan for large scale problems with adequate accuracy and efficiency is still highly challenging.
Recently, methods based on the Sinkhorn algorithm add an entropy regularizer to the prime problem and get a trade off between efficiency and accuracy.
In this paper, we propose a novel algorithm to further improve the efficiency and accuracy based on Nesterov's smoothing technique.
Basically, the non-smooth c-transform of the Kantorovich potential is approximated by the smooth Log-Sum-Exp function, which finally smooths the original non-smooth Kantorovich dual functional. The smooth Kantorovich functional can be optimized by the fast proximal gradient algorithm (FISTA) efficiently. Theoretically, the computational complexity of the proposed method is lower than
current estimation of the Sinkhorn algorithm in terms of the precision.
Empirically, compared with the Sinkhorn algorithm, our experimental results demonstrate that the proposed method achieves faster convergence and better accuracy with the same parameter.
Publisher
Association for the Advancement of Artificial Intelligence (AAAI)
Cited by
1 articles.
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