Scalable Unbalanced Optimal Transport using Generative Adversarial Networks
This work addresses scalable computation for unbalanced optimal transport, which is important for applications like population modeling, but it appears incremental as it builds on existing GAN frameworks and theoretical formulations.
The paper tackles the problem of unbalanced optimal transport by proposing a scalable method using generative adversarial networks, formulating it as learning a transport map and scaling factor with stochastic alternating gradient updates, and demonstrates its application to population modeling through numerical experiments.
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.