{"paper":{"title":"Gradient-free stochastic optimization of derivatives under strong convexity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alexandre B. Tsybakov, Arya Akhavan, Sirine Louati","submitted_at":"2026-07-08T10:30:57Z","abstract_excerpt":"We consider the problem of minimizing the $k$-th order partial derivative $f=\\partial_j^k g$ of an unknown function $g$ along a fixed coordinate direction $j$, based on noisy queries of $g$. Assuming that $g$ has H\\\"older regularity ${\\beta+k}$ for some $\\beta\\ge 2$, that $f$ is strongly convex on a compact convex set $\\Theta\\subset\\mathbb{R}^d$ and that $g$ and $f$ satisfy mild boundedness and Lipschitz regularity conditions on $\\Theta$, we propose a kernel-based estimator of $\\nabla f$ and analyze the projected stochastic gradient algorithm driven by this estimator. We obtain a non-asymptoti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07249","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/2607.07249/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"}