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Sharp Composition Bounds for Gaussian Differential Privacy via Edgeworth Expansion
Qinqing Zheng · Jinshuo Dong · Qi Long · Weijie Su

Thu Jul 16 06:00 AM -- 06:45 AM & Thu Jul 16 06:00 PM -- 06:45 PM (PDT) @
Datasets containing sensitive information are often sequentially analyzed by many algorithms and, accordingly, a fundamental question in differential privacy is concerned with how the overall privacy bound degrades under composition. To address this question, we introduce a family of analytical and sharp privacy bounds under composition using the Edgeworth expansion in the framework of the recently proposed $f$-differential privacy. In short, whereas the existing composition theorem, for example, relies on the central limit theorem, our new privacy bounds under composition gain improved tightness by leveraging the refined approximation accuracy of the Edgeworth expansion. Our approach is easy to implement and computationally efficient for any number of compositions. The superiority of these new bounds is confirmed by an asymptotic error analysis and an application to quantifying the overall privacy guarantees of noisy stochastic gradient descent used in training private deep neural networks.

Author Information

Qinqing Zheng (University of Pennsylvania)
Jinshuo Dong (University of Pennsylvania)
Qi Long (University of Pennsylvania)
Weijie Su (University of Pennsylvania)

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