SISTA: Learning Optimal Transport Costs under Sparsity Constraints

• Published in: Communications on pure and applied mathematics Vol. 76; no. 9; pp. 1659 - 1677
• Main Authors: Carlier, Guillaume, Dupuy, Arnaud, Galichon, Alfred, Sun, Yifei
• Format: Journal Article
• Language: English
• Published: Melbourne John Wiley & Sons Australia, Ltd 01.09.2023; John Wiley and Sons, Limited; Wiley
• Subjects: Economics and Finance; Humanities and Social Sciences; Iterative methods; Machine learning; Operating costs; Optimization; ISTA; Coordinate descent; Inverse optimal transport
• ISSN: 0010-3640; 1097-0312
• DOI: 10.1002/cpa.22047

In this paper, we describe a novel iterative procedure called SISTA to learn the underlying cost in optimal transport problems. SISTA is a hybrid between two classical methods, coordinate descent (“S”‐inkhorn) and proximal gradient descent (“ISTA”). It alternates between a phase of exact minimization over the transport potentials and a phase of proximal gradient descent over the parameters of the transport cost. We prove that this method converges linearly, and we illustrate on simulated examples that it is significantly faster than both coordinate descent and ISTA. We apply it to estimating a model of migration, which predicts the flow of migrants using country‐specific characteristics and pairwise measures of dissimilarity between countries. This application demonstrates the effectiveness of machine learning in quantitative social sciences. © 2022 Wiley Periodicals LLC.