{"paper":{"title":"Closing the Oracle-Complexity Gap in Derivative-Free Convex Optimization: A Near-Quadratic Lower Bound from Exact Function Values","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.OC","authors_text":"Phillip Kerger","submitted_at":"2026-07-14T23:45:21Z","abstract_excerpt":"We study the deterministic query complexity of minimizing a convex Lipschitz function over a $d$-dimensional Euclidean ball using only exact function values. At accuracy $\\Theta(d^{-1/2})$, the previously applicable lower bound was $\\Omega(d)$, inherited from the stronger full first-order oracle, while an upper bound from Protasov's value-only method requires $O(d^2\\log^2 d)$ evaluations. By providing a lower bound of $\\Omega(\\,\\frac{d^2}{\\log(d+1)})$ on the oracle complexity in this setting, we thereby close this gap dating back to 1996, up to polylogarithmic factors. Furthermore, we are able"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13335","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/2607.13335/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"}