  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.
