The central question studied in this paper is Rényi Differential Privacy (RDP) guarantees for general discrete local randomizers in the shuffle privacy model. In the shuffle model, each of the 𝑛 clients randomizes its response using a local differentially private (LDP) mechanism and the untrusted server only receives a random permutation (shuffle) of the client responses without association to each client. The principal result in this paper is the first direct RDP bounds for general discrete local randomization in the shuffle pri- vacy model, and we develop new analysis techniques for deriving our results which could be of independent interest. In applications, such an RDP guarantee is most useful when we use it for composing several private interactions. We numerically demonstrate that, for important regimes, with composition our bound yields an improve- ment in privacy guarantee by a factor of 8× over the state-of-the-art approximate Differential Privacy (DP) guarantee (with standard composition) for shuffle models. Moreover, combining with Pois- son subsampling, our result leads to at least 10× improvement over subsampled approximate DP with standard composition.
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Sharp Composition Bounds for Gaussian Differential Privacy via Edgeworth Expansion
Datasets containing sensitive information are often sequentially analyzed by many algorithms. This raises a fundamental question in differential privacy regarding 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 contrast to the existing composition theorems using 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.
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- PAR ID:
- 10215710
- Date Published:
- Journal Name:
- International Conference on Machine Learning
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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