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Optimal Transport (OT) naturally arises in many machine learningapplications, yet the heavy computational burden limits its wide-spread uses.To address the scalability issue, we propose an implicit generativelearning-based framework called SPOT (Scalable Push-forward of OptimalTransport). Specifically, we approximate the optimal transport plan by apushforward of a reference distribution, and cast the optimal transport probleminto a minimax problem. We then can solve OT problems efficiently using primaldual stochastic gradient-type algorithms. We also show that we can recover thedensity of the optimal transport plan using neural ordinary differentialequations. Numerical experiments on both synthetic and real datasets illustratethat SPOT is robust and has favorable convergence behavior. SPOT also allows usto efficiently sample from the optimal transport plan, which benefitsdownstream applications such as domain adaptation.

On Scalable and Efficient Computation of Large Scale Optimal Transport