# Approximating Euclidean by Imprecise Markov Decision Processes

arXiv: https://arxiv.org/abs/2006.14923 · HTML: https://mlsanity.com/paper/2006.14923/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2020.

## Built on by (most cited first, 4 of 4)

- [Decision-Making Under Uncertainty: Beyond Probabilities](https://mlsanity.com/paper/2303.05848/) (2023)
- [Shielded Reinforcement Learning for Hybrid Systems](https://mlsanity.com/paper/2308.14424/) (2023)
- [Imprecise Markov Semigroups and their Ergodicity](https://mlsanity.com/paper/2405.00081/) (2024)
- [Adaptive Probabilistic Shielding by Learning MDPs for Safe Reinforcement Learning](https://mlsanity.com/paper/2608.19836/) (2026)

## Abstract (arXiv)

Euclidean Markov decision processes are a powerful tool for modeling control problems under uncertainty over continuous domains. Finite state imprecise, Markov decision processes can be used to approximate the behavior of these infinite models. In this paper we address two questions: first, we investigate what kind of approximation guarantees are obtained when the Euclidean process is approximated by finite state approximations induced by increasingly fine partitions of the continuous state space. We show that for cost functions over finite time horizons the approximations become arbitrarily precise. Second, we use imprecise Markov decision process approximations as a tool to analyse and validate cost functions and strategies obtained by reinforcement learning. We find that, on the one hand, our new theoretical results validate basic design choices of a previously proposed reinforcement learning approach. On the other hand, the imprecise Markov decision process approximations reveal some inaccuracies in the learned cost functions.