We study the differentially private Empirical Risk Minimization (ERM) and Stochastic Convex Optimization (SCO) problems for non-smooth convex functions. We get a (nearly) optimal bound on the excess empirical risk and excess population loss with subquadratic gradient complexity. More precisely, our differentially private algorithm requires $O(\\frac{N^{3\/2}}{d^{1\/8}}+ \\frac{N^2}{d})$ gradient queries for optimal excess empirical risk, which is achieved with the help of subsampling and smoothing the function via convolution. This is the first subquadratic algorithm for the non-smooth case when $d$ is super constant. As a direct application, using the iterative localization approach of Feldman et al. \\cite{fkt20}, we achieve the optimal excess population loss for stochastic convex optimization problem, with $O(\\min\\{N^{5\/4}d^{1\/8},\\frac{ N^{3\/2}}{d^{1\/8}}\\})$ gradient queries. Our work makes progress towards resolving a question raised by Bassily et al. \\cite{bfgt20}, giving first algorithms for private ERM and SCO with subquadratic steps. We note that independently Asi et al. \\cite{afkt21} gave other algorithms for private ERM and SCO with subquadratic steps.<\/p>\n","protected":false},"excerpt":{"rendered":"
We study the differentially private Empirical Risk Minimization (ERM) and Stochastic Convex Optimization (SCO) problems for non-smooth convex functions. We get a (nearly) optimal bound on the excess empirical risk and excess population loss with subquadratic gradient complexity. More precisely, our differentially private algorithm requires $O(\\frac{N^{3\/2}}{d^{1\/8}}+ \\frac{N^2}{d})$ gradient queries for optimal excess empirical risk, which […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"NeurIPS 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