  This paper presents a widely applicable approach to solving (multi-marginal,
martingale) optimal transport and related problems via neural networks. The
core idea is to penalize the optimization problem in its dual formulation and
reduce it to a finite dimensional one which corresponds to optimizing a neural
network with smooth objective function. We present numerical examples from
optimal transport, martingale optimal transport, portfolio optimization under
uncertainty and generative adversarial networks that showcase the generality
and effectiveness of the approach.
