{"paper":{"title":"Empirical Risk Minimization in Non-interactive Local Differential Privacy: Efficiency and High Dimensional Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","stat.ML"],"primary_cat":"cs.LG","authors_text":"Di Wang, Jinhui Xu, Marco Gaboardi","submitted_at":"2018-02-12T14:52:24Z","abstract_excerpt":"In this paper, we study the Empirical Risk Minimization problem in the non-interactive local model of differential privacy. In the case of constant or low dimensionality ($p\\ll n$), we first show that if the ERM loss function is $(\\infty, T)$-smooth, then we can avoid a dependence of the sample complexity, to achieve error $\\alpha$, on the exponential of the dimensionality $p$ with base $1/\\alpha$ (i.e., $\\alpha^{-p}$), which answers a question in [smith 2017 interaction]. Our approach is based on polynomial approximation. Then, we propose player-efficient algorithms with $1$-bit communication"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04085","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}