## The Fundamental Price of Secure Aggregation in Differentially Private Federated Learning

### Wei-Ning Chen · Christopher Choquette Choo · Peter Kairouz · Ananda Suresh

##### Hall E #1017

Keywords: [ SA: Trustworthy Machine Learning ] [ SA: Privacy-preserving Statistics and Machine Learning ]

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Wed 20 Jul 3:30 p.m. PDT — 5:30 p.m. PDT

Spotlight presentation: SA: Privacy-preserving Statistics and Machine Learning
Wed 20 Jul 1:30 p.m. PDT — 3 p.m. PDT

Abstract: We consider the problem of training a $d$ dimensional model with distributed differential privacy (DP) where secure aggregation (SecAgg) is used to ensure that the server only sees the noisy sum of $n$ model updates in every training round. Taking into account the constraints imposed by SecAgg, we characterize the fundamental communication cost required to obtain the best accuracy achievable under $\varepsilon$ central DP (i.e. under a fully trusted server and no communication constraints). Our results show that $\tilde{O}\lp \min(n^2\varepsilon^2, d) \rp$ bits per client are both sufficient and necessary, and this fundamental limit can be achieved by a linear scheme based on sparse random projections. This provides a significant improvement relative to state-of-the-art SecAgg distributed DP schemes which use $\tilde{O}(d\log(d/\varepsilon^2))$ bits per client. Empirically, we evaluate our proposed scheme on real-world federated learning tasks. We find that our theoretical analysis is well matched in practice. In particular, we show that we can reduce the communication cost to under $1.78$ bits per parameter in realistic privacy settings without decreasing test-time performance. Our work hence theoretically and empirically specifies the fundamental price of using SecAgg.

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