Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework called SPOT (Scalable Push-forward of Optimal Transport). Specifically, we approximate the optimal transport plan by a pushforward of a reference distribution, and cast the optimal transport problem into a minimax problem. We then can solve OT problems efficiently using primal dual stochastic gradient-type algorithms. We also show that we can recover the density of the optimal transport plan using neural ordinary differential equations. Numerical experiments on both synthetic and real datasets illustrate that SPOT is robust and has favorable convergence behavior. SPOT also allows us to efficiently sample from the optimal transport plan, which benefits downstream applications such as domain adaptation.

提出了一种名为SPOT（Scalable Push-forward of Optimal Transport）的基于隐式生成学习的方法来解决“最优传输”（Optimal Transport，OT）中的可扩展性问题，该方法通过引入参考分布而近似最优传输计划，并将其转化为极小极大问题。实验结果表明SPOT系统具有可靠性和较好的收敛性，并允许从最优传输计划中高效采样，从而有利于领域适应等下游应用。

在大规模最优输运问题上的可扩展和高效计算