  Wasserstein distances are increasingly used in a wide variety of applications
in machine learning. Sliced Wasserstein distances form an important subclass
which may be estimated efficiently through one-dimensional sorting operations.
In this paper, we propose a new variant of sliced Wasserstein distance, study
the use of orthogonal coupling in Monte Carlo estimation of Wasserstein
distances and draw connections with stratified sampling, and evaluate our
approaches experimentally in a range of large-scale experiments in generative
modelling and reinforcement learning.
