{"paper":{"title":"Near-Optimal Lower Bounds for Exact Zeroth-Order Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chenheng Zhang, Haihan Zhang, Zhiquan Qi, Zhouchen Lin","submitted_at":"2026-07-18T00:04:07Z","abstract_excerpt":"The fundamental oracle limits of exact function value access remain poorly understood in zeroth-order optimization: even for canonical convex problems, the optimal joint dependence on dimension $d$ and accuracy $\\epsilon$ has remained unresolved. We resolve this question for arbitrary adaptive randomized algorithms minimizing nonsmooth $L_0$-Lipschitz convex functions over the $d$-dimensional Euclidean unit ball, where each query returns only the exact scalar value $f(\\mathbf x)$ of a fixed objective. With universal $L_0>0$, let $T_\\epsilon$ denote the minimum number of queries required to ret"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16558","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/2607.16558/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"}