{"paper":{"title":"Private PAC learning implies finite Littlestone dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CR","math.LO","stat.ML"],"primary_cat":"cs.LG","authors_text":"Maryanthe Malliaris, Noga Alon, Roi Livni, Shay Moran","submitted_at":"2018-06-04T04:35:29Z","abstract_excerpt":"We show that every approximately differentially private learning algorithm (possibly improper) for a class $H$ with Littlestone dimension~$d$ requires $\\Omega\\bigl(\\log^*(d)\\bigr)$ examples. As a corollary it follows that the class of thresholds over $\\mathbb{N}$ can not be learned in a private manner; this resolves open question due to [Bun et al., 2015, Feldman and Xiao, 2015]. We leave as an open question whether every class with a finite Littlestone dimension can be learned by an approximately differentially private algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00949","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"}