  Optimal transport (OT) theory underlies many emerging machine learning (ML)
methods nowadays solving a wide range of tasks such as generative modeling,
transfer learning and information retrieval. These latter works, however,
usually build upon a traditional OT setup with two distributions, while leaving
a more general multi-marginal OT formulation somewhat unexplored. In this
paper, we study the multi-marginal OT (MMOT) problem and unify several popular
OT methods under its umbrella by promoting structural information on the
coupling. We show that incorporating such structural information into MMOT
results in an instance of a different of convex (DC) programming problem
allowing us to solve it numerically. Despite high computational cost of the
latter procedure, the solutions provided by DC optimization are usually as
qualitative as those obtained using currently employed optimization schemes.
