{"paper":{"title":"Simple-regret rates and minimax optimality of fixed-prior expected improvement in Mat\\'ern and squared-exponential RKHSs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Emmanuel Vazquez, S\\'ebastien Petit","submitted_at":"2026-07-31T10:18:54Z","abstract_excerpt":"We study the expected improvement (EI) policy for minimizing a deterministic objective function $f$ on a nonempty compact set $\\mathcal X \\subset\\mathbb R^d$. We assume that $f$ belongs to the RKHS $\\mathcal H_k$ of a continuous positive-semidefinite kernel $k$ on $\\mathcal X$. Function values are observed exactly, and EI is computed from a fixed zero-mean Gaussian-process model with covariance $\\sigma^2k$. After an initial design, the policy queries a point whose EI is at least a fixed positive fraction of its maximum.\n  We identify the normalized posterior standard deviation at a candidate p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29245","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/2607.29245/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"}