The Sinkhorn algorithm (arXiv:1306.0895) is the state-of-the-art to compute approximations of optimal transport distances between discrete probability distributions, making use of an entropically regularized formulation of the problem. The algorithm is guaranteed to converge, no matter its initialization. This lead to little attention being paid to initializing it, and simple starting vectors like the n-dimensional one-vector are common choices. We train a neural network to compute initializations for the algorithm, which significantly outperform standard initializations. The network predicts a potential of the optimal transport dual problem, where training is conducted in an adversarial fashion using a second, generating network. The network is universal in the sense that it is able to generalize to any pair of distributions of fixed dimension. Furthermore, we show that for certain applications the network can be used independently.

翻译：Sinkhorn 算法( arXiv: 1306.0895) 是计算离散概率分布之间最佳运输距离近似值的最先进技术, 使用对问题进行随机化的正规化配方。 算法保证会趋同, 无论其初始化与否。 这导致对初始化的注意很少, 而像 n- 维一矢量这样的简单的起始矢量是常见的选择。 我们训练一个神经网络来计算算算算算初始化, 它大大超过标准初始化。 网络预测了最佳运输双重问题的潜力, 即利用第二个网络以对抗方式进行训练, 生成网络。 网络是普遍性的, 因为它能够对固定维量的分布作一对。 此外, 我们显示, 对于某些应用来说, 网络可以独立使用 。