mlsanityData to 14 Oct 2026

Local Differential Privacy with Correlated Noise Achieves Central-DP Optimal Cost

arXiv 2605.30476 ↗First posted 28 May 2026cs.IT cs.CR cs.LGcited by 0

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Abstract (arXiv)

We study privately estimating the sum of n user-held values in the presence of an honest-but-curious server. This motivates requiring privacy not only at data release but also throughout server-side computation. We therefore adopt the local (pure) differential privacy model, in which each user transmits a noise-perturbed value. It is well known that independent local noise typically incurs a substantial utility loss compared to the centralized model, where noise is added only after aggregation. We show that this gap is not fundamental. By carefully designing correlations among the locally added noise variables, we construct varepsilon-DP mechanisms whose estimation cost matches the optimal cost achievable in the centralized setting, up to an arbitrarily small error.

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References · 10

  1. 2016Communication-Efficient Learning of Deep Networks from Decentralized Datacited by 7,669
  2. 2016Deep Learning with Differential Privacycited by 2,728
  3. 2021Practical and Private (Deep) Learning without Sampling or Shufflingcited by 170
  4. 2022The Fundamental Price of Secure Aggregation in Differentially Private Federated Learningcited by 39
  5. 2022Optimal Algorithms for Mean Estimation under Local Differential Privacycited by 36
  6. 2021Efficient Differentially Private Secure Aggregation for Federated Learning via Hardness of Learning with Errorscited by 25
  7. 2024The Privacy Power of Correlated Noise in Decentralized Learningcited by 18
  8. 2025Correlated Noise Mechanisms for Differentially Private Learningcited by 14
  9. 2018Distributed Differentially-Private Algorithms for Matrix and Tensor Factorizationcited by 7
  10. 2024Correlated Privacy Mechanisms for Differentially Private Distributed Mean Estimationcited by 4

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