On differentially private stochastic convex optimization with heavy-Tailed data

Di Wang, Hanshen Xiao, Srini Devadas, Jinhui Xu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we consider the problem of de-signing Differentially Private (DP) algorithms for Stochastic Convex Optimization (SCO) on heavy-Tailed data. The irregularity of such data violates some key assumptions used in almost all existing DP-SCO and DP-ERM methods, re-sulting in failure to provide the DP guarantees. To better understand this type of challenges, we provide in this paper a comprehensive study of DP-SCO under various settings. First, we con-sider the case where the loss function is strongly convex and smooth. For this case, we propose a method based on the sample-And-Aggregate framework, which has an excess population risk of O( d3 n4 ) (after omitting other factors), where n is the sample size and d is the dimensional-ity of the data. Then, we show that with some additional assumptions on the loss functions, it is possible to reduce the expected excess popula-tion risk to O ( d2 n2 ). To lift these additional condi-tions, we also provide a gradient smoothing and trimming based scheme to achieve excess popula-tion risks of O ( d2 n2 ) and O( d 2 3 (n2) 13 ) for strongly convex and general convex loss functions, respec-tively, with high probability. Experiments sug-gest that our algorithms can effectively deal with the challenges caused by data irregularity.
Original languageEnglish (US)
Title of host publication37th International Conference on Machine Learning, ICML 2020
PublisherInternational Machine Learning Society (IMLS)
Pages10023-10033
Number of pages11
ISBN (Print)9781713821120
StatePublished - Jan 1 2020

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