{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/differentially-private-empirical-risk-1","title":"Differentially Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Bounds","arxiv_id":"1405.7085","date":"2014-05-27","proceeding":null,"authors":["Raef Bassily","Adam Smith","Abhradeep Thakurta"],"abstract":"In this paper, we initiate a systematic investigation of differentially\nprivate algorithms for convex empirical risk minimization. Various\ninstantiations of this problem have been studied before. We provide new\nalgorithms and matching lower bounds for private ERM assuming only that each\ndata point's contribution to the loss function is Lipschitz bounded and that\nthe domain of optimization is bounded. We provide a separate set of algorithms\nand matching lower bounds for the setting in which the loss functions are known\nto also be strongly convex.\n  Our algorithms run in polynomial time, and in some cases even match the\noptimal non-private running time (as measured by oracle complexity). We give\nseparate algorithms (and lower bounds) for $(\\epsilon,0)$- and\n$(\\epsilon,\\delta)$-differential privacy; perhaps surprisingly, the techniques\nused for designing optimal algorithms in the two cases are completely\ndifferent.\n  Our lower bounds apply even to very simple, smooth function families, such as\nlinear and quadratic functions. This implies that algorithms from previous work\ncan be used to obtain optimal error rates, under the additional assumption that\nthe contributions of each data point to the loss function is smooth. We show\nthat simple approaches to smoothing arbitrary loss functions (in order to apply\nprevious techniques) do not yield optimal error rates. In particular, optimal\nalgorithms were not previously known for problems such as training support\nvector machines and the high-dimensional median.","url_abs":"http://arxiv.org/abs/1405.7085v2","url_pdf":"http://arxiv.org/pdf/1405.7085v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"differentially-private-empirical-risk-1","repo_url":"https://github.com/sunblaze-ucb/dpml-benchmark","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1405.7085","atlas_url":"https://app.syntology.ai/?focus=1405.7085","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}