  We introduce COT-GAN, an adversarial algorithm to train implicit generative
models optimized for producing sequential data. The loss function of this
algorithm is formulated using ideas from Causal Optimal Transport (COT), which
combines classic optimal transport methods with an additional temporal
causality constraint. Remarkably, we find that this causality condition
provides a natural framework to parameterize the cost function that is learned
by the discriminator as a robust (worst-case) distance, and an ideal mechanism
for learning time dependent data distributions. Following Genevay et al.\
(2018), we also include an entropic penalization term which allows for the use
of the Sinkhorn algorithm when computing the optimal transport cost. Our
experiments show effectiveness and stability of COT-GAN when generating both
low- and high-dimensional time series data. The success of the algorithm also
relies on a new, improved version of the Sinkhorn divergence which demonstrates
less bias in learning.

Machine Learning;Machine Learning