Differentially Private SGDA for Minimax Problems

Zhenhuan Yang, Shu Hu, Yunwen Lei, Kush R. Varshney, Siwei Lyu, Yiming Ying

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review

3 Citations (Scopus)

Abstract

Stochastic gradient descent ascent (SGDA) and its variants have been the workhorse for solving minimax problems. However, in contrast to the well-studied stochastic gradient descent (SGD) with differential privacy (DP) constraints, there is little work on understanding the generalization (utility) of SGDA with DP constraints. In this paper, we use the algorithmic stability approach to establish the generalization (utility) of DP-SGDA in different settings. In particular, for the convex-concave setting, we prove that the DP-SGDA can achieve an optimal utility rate in terms of the weak primal-dual population risk in both smooth and non-smooth cases. To our best knowledge, this is the first-ever-known result for DP-SGDA in the non-smooth case. We further provide its utility analysis in the nonconvex-strongly-concave setting which is the first-ever-known result in terms of the primal population risk. The convergence and generalization results for this nonconvex setting are new even in the non-private setting. Finally, numerical experiments are conducted to demonstrate the effectiveness of DP-SGDA for both convex and nonconvex cases.

Original languageEnglish
Title of host publicationProceedings of the 38th Conference on Uncertainty in Artificial Intelligence, UAI 2022
EditorsJames Cussens, Kun Zhang
PublisherML Research Press
Pages2192-2202
Number of pages11
ISBN (Print)9781713863298
Publication statusPublished - Aug 2022
Event38th Conference on Uncertainty in Artificial Intelligence, UAI 2022 - Eindhoven, Netherlands
Duration: 1 Aug 20225 Aug 2022
https://proceedings.mlr.press/v180/ (Conference proceedings)

Publication series

NameProceedings of Machine Learning Research
Volume180
ISSN (Print)2640-3498

Conference

Conference38th Conference on Uncertainty in Artificial Intelligence, UAI 2022
Country/TerritoryNetherlands
CityEindhoven
Period1/08/225/08/22
Internet address

Scopus Subject Areas

  • Artificial Intelligence

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