Safe Learning for Uncertainty-Aware Planning via Interval MDP Abstraction

TL;DR

This paper presents an abstraction-based method for safe, uncertainty-aware planning in stochastic systems, using Interval MDPs derived from Gaussian process regression to refine bounds and synthesize control policies.

Contribution

It introduces an iterative approach combining IMDP abstractions, path sampling, and heuristics to improve planning under uncertainty for systems with unknown dynamics.

Findings

Successfully applied to mobile robot navigation case study.

Achieved high-confidence bounds on system behavior.

Enhanced safety and performance in uncertain environments.

Abstract

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.