Learning Cost Functions for Optimal Transport

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 regularizatio...

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Bibliographic Details
Published inarXiv.org
Main Authors Ma, Shaojun, Sun, Haodong, Ye, Xiaojing, Zha, Hongyuan, Zhou, Haomin
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 05.07.2021
Subjects
Algorithms
Artificial neural networks
Computational geometry
Convexity
Cost function
Iterative methods
Machine learning
Neural networks
Optimization
Regularization
Transportation planning
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Summary: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.
ISSN:2331-8422