{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-simple-and-efficient-sampling-based","title":"A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis","arxiv_id":"2112.05745","date":"2021-12-10","proceeding":null,"authors":["Thomas Lew","Lucas Janson","Riccardo Bonalli","Marco Pavone"],"abstract":"In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of dynamical systems. By sampling inputs, evaluating their images in the true reachable set, and taking their $\\epsilon$-padded convex hull as a set estimator, this algorithm applies to general problem settings and is simple to implement. Our main contribution is the derivation of asymptotic and finite-sample accuracy guarantees using random set theory. This analysis informs algorithmic design to obtain an $\\epsilon$-close reachable set approximation with high probability, provides insights into which reachability problems are most challenging, and motivates safety-critical applications of the technique. On a neural network verification task, we show that this approach is more accurate and significantly faster than prior work. Informed by our analysis, we also design a robust model predictive controller that we demonstrate in hardware experiments.","url_abs":"https://arxiv.org/abs/2112.05745v3","url_pdf":"https://arxiv.org/pdf/2112.05745v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-simple-and-efficient-sampling-based","repo_url":"https://github.com/stanfordasl/randup","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"a-simple-and-efficient-sampling-based","repo_url":"https://github.com/stanfordasl/stochasticedl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2112.05745","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2112.05745"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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