{"paper":{"title":"Information-Theoretic Upper Bounds for Deterministic Noise in Zeroth-Order Convex Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexander Gasnikov, Dmitry Pasechnyuk-Vilensky, Igor Pavlov, Martin Tak\\'a\\v{c}","submitted_at":"2023-06-28T17:06:52Z","abstract_excerpt":"We study deterministic adversarial noise in zeroth-order convex optimization on Euclidean balls. The maximum admissible level of noise is the largest uniform error in function-value queries for which polynomial-query optimization remains possible. We convert the Risteski-Li information-theoretic obstruction for approximately convex optimization into deterministic noisy-oracle upper bounds on this quantity.\n  The conversion gives the Lipschitz convex MALN upper bound with the Risteski-Li dimension dependence. A localized conic-collar embedding gives the corresponding Lipschitz strongly convex b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.16371","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.16371/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}