Kantorovich Rubinstein Distance

The Kantorovich-Rubinstein distance (a specific type of Wasserstein distance) quantifies the difference between probability distributions, considering the underlying geometry and topology. Current research focuses on efficient computation of this distance, particularly for high-dimensional data and complex settings like Markov decision processes, often employing techniques like mirror descent algorithms and reduced basis methods to improve computational speed and scalability. These advancements are impacting diverse fields, including generative adversarial networks (GANs) for image generation, transfer learning in reinforcement learning, and economic modeling of resource allocation problems.