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.
@article{arxiv.2202.01358,
title = {Safe Learning for Uncertainty-Aware Planning via Interval MDP Abstraction},
author = {Jesse Jiang and Ye Zhao and Samuel Coogan},
journal= {arXiv preprint arXiv:2202.01358},
year = {2022}
}
Comments
8 pages, 3 figures; accepted to IEEE Control Systems Letters