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A generalization of the Wasserstein metric, the integrated transportationdistance, establishes a novel distance between probability kernels of Markovsystems. This metric serves as the foundation for an efficient approximationtechnique, enabling the replacement of the original system's kernel with akernel with a discrete support of limited cardinality. To facilitate practicalimplementation, we present a specialized dual algorithm capable of constructingthese approximate kernels quickly and efficiently, without requiringcomputationally expensive matrix operations. Finally, we demonstrate theefficacy of our method through several illustrative examples, showcasing itsutility in practical scenarios. This advancement offers new possibilities forthe streamlined analysis and manipulation of stochastic systems represented bykernels.

Fast Dual Subgradient Optimization of the Integrated Transportation Distance Between Stochastic Kernels