{"paper":{"title":"Public-data Assisted Private Stochastic Optimization: Power and Limitations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CR","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Crist\\'obal Guzm\\'an, Enayat Ullah, Michael Menart, Raef Bassily, Raman Arora","submitted_at":"2024-03-06T17:06:11Z","abstract_excerpt":"We study the limits and capability of public-data assisted differentially private (PA-DP) algorithms. Specifically, we focus on the problem of stochastic convex optimization (SCO) with either labeled or unlabeled public data. For complete/labeled public data, we show that any $(\\epsilon,\\delta)$-PA-DP has excess risk $\\tilde{\\Omega}\\big(\\min\\big\\{\\frac{1}{\\sqrt{n_{\\text{pub}}}},\\frac{1}{\\sqrt{n}}+\\frac{\\sqrt{d}}{n\\epsilon} \\big\\} \\big)$, where $d$ is the dimension, ${n_{\\text{pub}}}$ is the number of public samples, ${n_{\\text{priv}}}$ is the number of private samples, and $n={n_{\\text{pub}}}+"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.03856","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/2403.03856/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"}