Optimal Transport (OT) distances such as Wasserstein have been used in several areas such as GANs and domain adaptation. OT, however, is very sensitive to outliers (samples with large noise) in the data since in its objective function, every sample, including outliers, is weighed similarly due to the marginal constraints. To remedy this issue, robust formulations of OT with unbalanced marginal constraints have previously been proposed. However, employing these methods in deep learning problems such as GANs and domain adaptation is challenging due to the instability of their dual optimization solvers. In this paper, we resolve these issues by deriving a computationally-efficient dual form of the robust OT optimization that is amenable to modern deep learning applications. We demonstrate the effectiveness of our formulation in two applications of GANs and domain adaptation. Our approach can train state-of-the-art GAN models on noisy datasets corrupted with outlier distributions. In particular, our optimization computes weights for training samples reflecting how difficult it is for those samples to be generated in the model. In domain adaptation, our robust OT formulation leads to improved accuracy compared to the standard adversarial adaptation methods. Our code is available at https://github.com/yogeshbalaji/robustOT.

翻译：最佳运输(OT)距离,如瓦森斯坦(Wasserstein)等最佳运输(OT)距离,已在诸如GANs和域适应等若干领域使用过。然而,OT对数据中的外部值(有大噪音的样本)非常敏感,因为在其客观功能中,每个样本,包括外部值,都因边际限制而受到类似的权衡。为了纠正这一问题,以前曾提议过在诸如瓦森斯坦(Wasserstein)等深层学习问题中采用强力运输(OT)配方的强力配方,如GANs和域适应(域)等。然而,采用这些方法在诸如GANs等深层学习问题中具有挑战性。在本文件中,我们通过产生一种具有计算效率的双重形式的强力OT优化方法来解决这些问题。在现代深层学习应用中,我们通过两种应用GANs和域调适应用的方式展示了我们的配方的效能。我们的方法可以训练最先进的GAN模型的热度模型模型,特别是,我们最优化的样品的计算重量表明这些样品在模型中产生的难度。在如何产生。在模型中,在域适应中,我们的坚固的OT/BEBS/ODGEBAGUBS/OBS的配法是改进了现有标准的精确性准则。