# Data-driven abstractions via adaptive refinements and a Kantorovich metric [extended version]

arXiv: https://arxiv.org/abs/2303.17618 · HTML: https://mlsanity.com/paper/2303.17618/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 30 Mar 2023.

## Builds on (most cited first, 14 of 14)

- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [A storm is Coming: A Modern Probabilistic Model Checker](https://mlsanity.com/paper/1702.04311/) (2017)
- [Data-Driven Model Predictive Control with Stability and Robustness Guarantees](https://mlsanity.com/paper/1906.04679/) (2019)
- [Perturbation theory for Markov chains via Wasserstein distance](https://mlsanity.com/paper/1503.04123/) (2015)
- [Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractions](https://mlsanity.com/paper/2301.01526/) (2023)
- [On Computing the Total Variation Distance of Hidden Markov Models](https://mlsanity.com/paper/1804.06170/) (2018)
- [Constructing MDP Abstractions Using Data with Formal Guarantees](https://mlsanity.com/paper/2206.14402/) (2022)
- [Symbolic Abstractions From Data: A PAC Learning Approach](https://mlsanity.com/paper/2104.13901/) (2021)
- [On Abstraction-Based Controller Design With Output Feedback](https://mlsanity.com/paper/2002.02687/) (2020)
- [Asynchronous l-Complete Approximations](https://mlsanity.com/paper/1402.5759/) (2014)
- [Data-driven memory-dependent abstractions of dynamical systems](https://mlsanity.com/paper/2212.01926/) (2022)
- [A data-driven method for computing polyhedral invariant sets of black-box switched linear systems](https://mlsanity.com/paper/2009.10984/) (2020)
- [Learning stability guarantees for data-driven constrained switching linear systems](https://mlsanity.com/paper/2205.00696/) (2022)
- [Black-box stability analysis of hybrid systems with sample-based multiple Lyapunov functions](https://mlsanity.com/paper/2205.00699/) (2022)

## Built on by (most cited first, 3 of 3)

- [Formal Control for Uncertain Systems via Contract-Based Probabilistic Surrogates (Extended Version)](https://mlsanity.com/paper/2506.16971/) (2025)
- [A Cantor-Kantorovich Metric Between Markov Decision Processes with Application to Transfer Learning](https://mlsanity.com/paper/2407.08324/) (2024)
- [Kernel-Based Learning of Safety Barriers](https://mlsanity.com/paper/2601.12002/) (2026)

## Abstract (arXiv)

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 as a loss function. Our technique is prone to data-driven frameworks, but not restricted to. We also study properties of the above mentioned metric between Markov chains, which we believe could be of application for wider purpose. 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.