Learning cost function for optimal transport

作     者：Ma, Shaojun Sun, Haodong Ye, Xiaojing Zha, Hongyuan Zhou, Haomin 

作者机构：School of Mathematics Georgia Institute of Technology AtlantaGA30332 United States Department of Mathematics and Statistics Georgia State University AtlantaGA30303 United States School of Data Science Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen Guangdong 518172 China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2020年

核心收录：

主　　题：Cost functions 

摘      要：Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem, which can be further augmented by any customizable regularization. We provide a comprehensive characterization of the properties of inverse OT, including uniqueness of solutions. We also develop two numerical algorithms, one is a fast matrix scaling method based on the Sinkhorn-Knopp algorithm for discrete OT, and the other one is a learning based algorithm that parameterizes the cost function as a deep neural network for continuous OT. The novel framework proposed in the work avoids repeatedly solving a forward OT in each iteration which has been a thorny computational bottleneck for the bi-level optimization in existing inverse OT approaches. Numerical results demonstrate promising efficiency and accuracy advantages of the proposed algorithms over existing state-of-the-art methods. Copyright © 2020, The Authors. All rights reserved.