Data-driven abstractions via adaptive refinements and a Kantorovich metric

We introduce an adaptive refinement procedure for smart and scalable abstraction of dynamical systems. Our technique relies on partitioning the state space depending on the observation of future outputs. However, this knowledge is dynamically constructed in an adaptive, asymmetric way. In order to learn the optimal structure, we define a Kantorovich-inspired metric between Markov chains, and we use it to guide the state partition refinement. Our technique is prone to datadriven frameworks, but not restricted to. We also study properties of the above mentioned metric between Markov chains, which we believe could be of broader interest. We propose an algorithm to approximate it, and we show that our method yields a much better computational complexity than using classical linear programming techniques.