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

Computation of optimal transport and related hedging problems via penalization and neural networks