# A Scenario Approach to Risk-Aware Safety-Critical System Verification

arXiv: https://arxiv.org/abs/2203.02595 · HTML: https://mlsanity.com/paper/2203.02595/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2022.

## Built on by (most cited first, 5 of 5)

- [How Generalizable Is My Behavior Cloning Policy? A Statistical Approach to Trustworthy Performance Evaluation](https://mlsanity.com/paper/2405.05439/) (2024)
- [Sample-Based Bounds for Coherent Risk Measures: Applications to Policy Synthesis and Verification](https://mlsanity.com/paper/2204.09833/) (2022)
- [Risk-Awareness in Learning Neural Controllers for Temporal Logic Objectives](https://mlsanity.com/paper/2210.07439/) (2022)
- [Verifiable Learned Behaviors via Motion Primitive Composition: Applications to Scooping of Granular Media](https://mlsanity.com/paper/2309.14894/) (2023)
- [Towards provable probabilistic safety for scalable embodied AI systems](https://mlsanity.com/paper/2506.05171/) (2025)

## Abstract (arXiv)

With the growing interest in deploying robots in unstructured and uncertain environments, there has been increasing interest in factoring risk into safety-critical control development. Similarly, the authors believe risk should also be accounted in the verification of these controllers. In pursuit of sample-efficient methods for uncertain black-box verification then, we first detail a method to estimate the Value-at-Risk of arbitrary scalar random variables without requiring textitapriori knowledge of its distribution. Then, we reformulate the uncertain verification problem as a Value-at-Risk estimation problem making use of our prior results. In doing so, we provide fundamental sampling requirements to bound with high confidence the volume of states and parameters for a black-box system that could potentially yield unsafe phenomena. We also show that this procedure works independent of system complexity through simulated examples of the Robotarium.