Scalable Unbalanced Optimal Transport using Generative Adversarial Networks

Abstract

Generative adversarial networks (GANs) are an expressive class of neural generative models with tremendous success in modeling high-dimensional continuous measures. In this paper, we present a scalable method for unbalanced optimal transport (OT) based on the generative-adversarial framework. We formulate unbalanced OT as a problem of simultaneously learning a transport map and a scaling factor that push a source measure to a target measure in a cost-optimal manner. In addition, we propose an algorithm for solving this problem based on stochastic alternating gradient updates, similar in practice to GANs. We also provide theoretical justification for this formulation, showing that it is closely related to an existing static formulation by Liero et al. (2018), and perform numerical experiments demonstrating how this methodology can be applied to population modeling.

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Cited by in corpus (5)

• Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptation
• Partial Optimal Transport with Applications on Positive-Unlabeled Learning
• On Scalable and Efficient Computation of Large Scale Optimal Transport
• Potential Flow Generator with $L_2$ Optimal Transport Regularity for Generative Models
• Large-Scale Optimal Transport via Adversarial Training with Cycle-Consistency