{"paper":{"title":"High-Probability Guarantees for Random Zeroth-Order Gradient Descent on Smooth Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Haishan Ye","submitted_at":"2026-05-26T04:56:24Z","abstract_excerpt":"Randomized zeroth-order methods are classically analyzed in expectation, but a black-box Markov conversion can give misleading high-probability guarantees, in particular by forcing the finite-difference smoothing radius to shrink with the confidence parameter. This paper gives a direct finite-horizon high-probability analysis of a two-query Gaussian finite-difference method for deterministic objectives with Lipschitz gradients. The method uses the classical two-point estimator together with the normalized stepsize \\(\\eta_t=1/(4L\\norm{\\bu_t}^2)\\). We prove that it finds an \\(\\varepsilon\\)-subop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26547","kind":"arxiv","version":1},"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/2605.26547/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"}