Probably Approximately Correct (PAC) Guarantees for Data-Driven Reachability Analysis: A Theoretical and Empirical Comparison
Abstract
Reachability analysis evaluates system safety, by identifying the set of states a system may evolve within over a finite time horizon. In contrast to model-based reachability analysis, data-driven reachability analysis estimates reachable sets and derives probabilistic guarantees directly from data. Several popular techniques for validating reachable sets -- conformal prediction, scenario optimization, and the holdout method -- admit similar Probably Approximately Correct (PAC) guarantees. We establish a formal connection between these PAC bounds and present an empirical case study on reachable sets to illustrate the computational and sample trade-offs associated with these methods. We argue that despite the formal relationship between these techniques, subtle differences arise in both the interpretation of guarantees and the parameterization. As a result, these methods are not generally interchangeable. We conclude with practical advice on the usage of these methods.
Cite
@article{arxiv.2604.02953,
title = {Probably Approximately Correct (PAC) Guarantees for Data-Driven Reachability Analysis: A Theoretical and Empirical Comparison},
author = {Elizabeth Dietrich and Hanna Krasowski and Murat Arcak},
journal= {arXiv preprint arXiv:2604.02953},
year = {2026}
}