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In this paper, we introduce a primal-dual algorithm for solving (martingale)optimal transportation problems, with cost functions satisfying the twistcondition, close to the one that has been used recently for training generativeadversarial networks. As some additional applications, we consider anomalydetection and automatic generation of financial data.

(Martingale) Optimal Transport And Anomaly Detection With Neural Networks: A Primal-dual Algorithm