Infinitely Divisible Noise in the Low Privacy Regime

• URL: http://arxiv.org/abs/2110.06559v1
• Date: Wed, 13 Oct 2021 08:16:43 GMT
• Title: Infinitely Divisible Noise in the Low Privacy Regime
• Authors: Rasmus Pagh, Nina Mesing Stausholm
• Abstract summary: Federated learning, in which training data is distributed among users and never shared, has emerged as a popular approach to privacy-preserving machine learning. We present the first divisible infinitely noise distribution for real-valued data that achieves $varepsilon$-differential privacy.
• Score: 9.39772079241093
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Federated learning, in which training data is distributed among users and never shared, has emerged as a popular approach to privacy-preserving machine learning. Cryptographic techniques such as secure aggregation are used to aggregate contributions, like a model update, from all users. A robust technique for making such aggregates differentially private is to exploit infinite divisibility of the Laplace distribution, namely, that a Laplace distribution can be expressed as a sum of i.i.d. noise shares from a Gamma distribution, one share added by each user. However, Laplace noise is known to have suboptimal error in the low privacy regime for $\varepsilon$-differential privacy, where $\varepsilon > 1$ is a large constant. In this paper we present the first infinitely divisible noise distribution for real-valued data that achieves $\varepsilon$-differential privacy and has expected error that decreases exponentially with $\varepsilon$.

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