Importance Sampling for Statistical Certification of Viable Initial Sets

[2604.02939] Importance Sampling for Statistical Certification of Viable Initial Sets Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Electrical Engineering and Systems Science > Systems and Control arXiv:2604.02939 (eess) [Submitted on 3 Apr 2026 ( v1 ), last revised 14 Aug 2026 (this version, v2)] Title: Importance Sampling for Statistical Certification of Viable Initial Sets Authors: Elizabeth Dietrich , Hanna Krasowski , Vegard Flovik , Murat Arcak View a PDF of the paper titled Importance Sampling for Statistical Certification of Viable Initial Sets, by Elizabeth Dietrich and Hanna Krasowski and Vegard Flovik and Murat Arcak View PDF Abstract: We study the problem of statistically certifying viable initial sets (VISs)---sets of initial conditions whose trajectories satisfy a given control specification. While VISs can be obtained from model-based methods, these methods typically rely on simplified models. We propose a simulation-based framework to certify VISs by estimating the probability of specification violations under a high-fidelity or black-box model. Since detecting these violations may be challenging due to their scarcity, we propose a sample-efficient framework that leverages importance sampling to target high-risk regions. We derive an empirical Bernstein inequality for weighted random variables, enabling finite-sample guarantees for importance sampling estimators. We demonstrate the proposed approach on two systems and show improved convergence of the resulting bounds on an adaptive cruise control benchmark. Subjects: Systems and Control (eess.SY) Cite as: arXiv:2604.02939 [eess.SY] (or arXiv:2604.02939v2 [eess.SY] for this version) https://doi.org/10.48550/arXiv.2604.02939 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Elizabeth Dietrich [ view email ] [v1] Fri, 3 Apr 2026 10:15:44 UTC (285 KB) [v2] Fri, 14 Aug 2026 22:54:54 UTC (1,005 KB) Full-text links: Access Paper: View a PDF of the paper titled Importance Sampling for Statistical Certification of Viable Initial Sets, by Elizabeth Dietrich and Hanna Krasowski and Vegard Flovik and Murat Arcak View PDF TeX Source view license Current browse context: eess.SY < prev | next > new | recent | 2026-04 Change to browse by: cs cs.SY eess References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Confidence Sequences for Online Statistical Model Checking of Markov Decision Processes#307062
• Probabilistic algorithm for testing primality#490237
• Boundary Loss and the Born Rule: Pre-Numerical Probability-Status in Deterministic Systems#707598
• Active Calibration of Reachable Sets Using Approximate Pick-to-Learn#927267
• Decidable Formulas Of Intuitionistic Primitive Recursive Arithmetic#764848