# Safe Learning for Uncertainty-Aware Planning via Interval MDP Abstraction

arXiv: https://arxiv.org/abs/2202.01358 · HTML: https://mlsanity.com/paper/2202.01358/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2022.

## Built on by (most cited first, 2 of 2)

- [Data-Driven Abstractions via Binary-Tree Gaussian Processes for Formal Verification](https://mlsanity.com/paper/2407.21029/) (2024)
- [VeRecycle: Reclaiming Guarantees from Probabilistic Certificates for Stochastic Dynamical Systems after Change](https://mlsanity.com/paper/2505.14001/) (2025)

## Abstract (arXiv)

We study the problem of refining satisfiability bounds for partially-known stochastic systems against planning specifications defined using syntactically co-safe Linear Temporal Logic (scLTL). We propose an abstraction-based approach that iteratively generates high-confidence Interval Markov Decision Process (IMDP) abstractions of the system from high-confidence bounds on the unknown component of the dynamics obtained via Gaussian process regression. In particular, we develop a synthesis strategy to sample the unknown dynamics by finding paths which avoid specification-violating states using a product IMDP. We further provide a heuristic to choose among various candidate paths to maximize the information gain. Finally, we propose an iterative algorithm to synthesize a satisfying control policy for the product IMDP system. We demonstrate our work with a case study on mobile robot navigation.