Interior-Point Methods Strike Back: Solving the Wasserstein Barycenter Problem
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Publication:6319640
arXiv1905.12895MaRDI QIDQ6319640
Author name not available (Why is that?)
Publication date: 30 May 2019
Abstract: Computing the Wasserstein barycenter of a set of probability measures under the optimal transport metric can quickly become prohibitive for traditional second-order algorithms, such as interior-point methods, as the support size of the measures increases. In this paper, we overcome the difficulty by developing a new adapted interior-point method that fully exploits the problem's special matrix structure to reduce the iteration complexity and speed up the Newton procedure. Different from regularization approaches, our method achieves a well-balanced tradeoff between accuracy and speed. A numerical comparison on various distributions with existing algorithms exhibits the computational advantages of our approach. Moreover, we demonstrate the practicality of our algorithm on image benchmark problems including MNIST and Fashion-MNIST.
Has companion code repository: https://gitlab.com/ZXiong/wasserstein-barycenter
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