Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into a set of input nodes and collected from a set of output nodes while minimizing the expected transportation cost together with a paths relative entropy regularization term, providing a randomized routing policy. The main advantage of this new formulation is the fact that it can easily accommodate edge flow capacity constraints which commonly occur in real-world problems. The resulting optimal routing policy, i.e., the probability distribution of following an edge in each node, is Markovian and is computed by constraining the input and output flows to the prescribed marginal probabilities thanks to a variant of the algorithm developed in [8]. Besides, experimental comparisons with other recently developed techniques show that the distance measure between nodes derived from the introduced model provides competitive results on semi-supervised classification tasks.

翻译：在 [21, 23] 之后,本项工作调查了一种新的相对正正正常规算法,用于在随机最短路径的形式主义范围内解决图形问题的最佳传输。更准确地说,单位流被注入一组输入节点,从一组输出节点中收集,同时尽量减少预期的运输成本,同时提供一个路径相对加密正规化的术语,提供随机化路线政策。这一新公式的主要优点是,它能够很容易地适应现实世界问题中常见的边缘流动能力限制。由此产生的最佳路线政策,即每个节点边缘的概率分布是Markovian,其计算方法是将输入和输出流限制到[8] 中开发的算法的变量所规定的边际概率。此外,与其他最近开发的技术进行的实验性比较表明,从采用的模式中得出的节点之间的距离测量方法在半监督分类任务上提供了竞争性的结果。