{"paper":{"title":"Private Convex Optimization via Exponential Mechanism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","cs.LG","math.OC","math.PR"],"primary_cat":"cs.DS","authors_text":"Daogao Liu, Sivakanth Gopi, Yin Tat Lee","submitted_at":"2022-03-01T06:51:03Z","abstract_excerpt":"In this paper, we study private optimization problems for non-smooth convex functions $F(x)=\\mathbb{E}_i f_i(x)$ on $\\mathbb{R}^d$. We show that modifying the exponential mechanism by adding an $\\ell_2^2$ regularizer to $F(x)$ and sampling from $\\pi(x)\\propto \\exp(-k(F(x)+\\mu\\|x\\|_2^2/2))$ recovers both the known optimal empirical risk and population loss under $(\\epsilon,\\delta)$-DP. Furthermore, we show how to implement this mechanism using $\\widetilde{O}(n \\min(d, n))$ queries to $f_i(x)$ for the DP-SCO where $n$ is the number of samples/users and $d$ is the ambient dimension. We also give "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.00263","kind":"arxiv","version":2},"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/2203.00263/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"}