ServiceNow Research

Adversarial Computation of Optimal Transport Maps


Computing optimal transport maps between high-dimensional and continuous distributions is a challenging problem in optimal transport (OT). Generative adversarial networks (GANs) are powerful generative models which have been successfully applied to learn maps across high-dimensional domains. However, little is known about the nature of the map learned with a GAN objective. To address this problem, we propose a generative adversarial model in which the discriminator’s objective is the 2-Wasserstein metric. We show that during training, our generator follows the W2-geodesic between the initial and the target distributions. As a consequence, it reproduces an optimal map at the end of training. We validate our approach empirically in both low-dimensional and high-dimensional continuous settings, and show that it outperforms prior methods on image data.

Sai Rajeswar Mudumba
Sai Rajeswar Mudumba
Research Scientist

Research Scientist at Low Data Learning located at Montreal, QC, Canada.