{"paper":{"title":"Distributionally Robust Safety Under Arbitrary Uncertainties: A Safety Filtering Approach","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Backup-based safety filtering reduces distributionally robust certification to a one-dimensional search over switching time.","cross_cats":["cs.SY","eess.SY"],"primary_cat":"cs.RO","authors_text":"Daniel M. Cherenson, Dimitra Panagou, Haejoon Lee, Taekyung Kim","submitted_at":"2026-05-13T04:11:58Z","abstract_excerpt":"In this work, we study how to ensure probabilistic safety for nonlinear systems under distributional ambiguity. Our approach builds on a backup-based safety filtering framework that switches between a high-performance nominal policy and a certified backup policy to ensure safety. To handle arbitrary uncertainties from ambiguous distributions, i.e., where the distribution is not of specific structure and the true distribution is unknown, we adopt a distributionally robust (DR) formulation using Wasserstein ambiguity sets. Rather than solving a high-dimensional DR trajectory optimization problem"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we exploit the structure of backup-based safety filtering to reduce safety certification to a one-dimensional search over the switching time between nominal and backup policies. We then develop a sampling-based certification procedure with finite-sample guarantees, where empirical failure probabilities are compared against a Wasserstein-inflated threshold.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The true uncertainty distribution lies within the chosen Wasserstein ambiguity set around the empirical distribution, and the backup policy remains certified safe under the worst-case distribution in that set.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A backup-based safety filter combined with Wasserstein ambiguity sets reduces probabilistic safety certification for nonlinear systems to a one-dimensional search with finite-sample guarantees.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Backup-based safety filtering reduces distributionally robust certification to a one-dimensional search over switching time.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ca72d2960fc558276f5dacb88cf949419fdda0ccdd06dcc9148d470aff570951"},"source":{"id":"2605.12974","kind":"arxiv","version":1},"verdict":{"id":"37df38e2-da23-48a9-8e06-ae57fea041f7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:32:15.323813Z","strongest_claim":"we exploit the structure of backup-based safety filtering to reduce safety certification to a one-dimensional search over the switching time between nominal and backup policies. We then develop a sampling-based certification procedure with finite-sample guarantees, where empirical failure probabilities are compared against a Wasserstein-inflated threshold.","one_line_summary":"A backup-based safety filter combined with Wasserstein ambiguity sets reduces probabilistic safety certification for nonlinear systems to a one-dimensional search with finite-sample guarantees.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The true uncertainty distribution lies within the chosen Wasserstein ambiguity set around the empirical distribution, and the backup policy remains certified safe under the worst-case distribution in that set.","pith_extraction_headline":"Backup-based safety filtering reduces distributionally robust certification to a one-dimensional search over switching time."},"references":{"count":37,"sample":[{"doi":"","year":2024,"title":"Advances in the theory of control barrier func- tions: Addressing practical challenges in safe control synthesis for autonomous and robotic systems,","work_id":"edf555c9-62ab-43a2-ad4c-0deaf34a0b20","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"The safety filter: A unified view of safety-critical control in autonomous systems","work_id":"2c18d82a-06e9-4d2f-ae2b-0977c746dc29","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Hamilton- jacobi reachability: A brief overview and recent advances,","work_id":"1cd35745-2738-4fc0-96af-2925fc927e9c","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Control barrier functions: Theory and applications,","work_id":"0ac48f00-775a-482a-84ea-92f291ef3545","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Robust safety under stochastic uncertainty with discrete-time control barrier functions","work_id":"b49e8448-3d52-40f1-ac92-113d1edd90ed","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":37,"snapshot_sha256":"6c79e85e665a3e5779ef18cbcd17d4174b35b0ce6a18f2a068b3e9391c13573d","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"0b56d68827308864919cf2d3ad0be309e6a435c55f2ecf934473632a492437ba"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}