mlsanityData to 7 Oct 2026

A Van Trees Lower Bound for Fully Interactive Differentially Private Federated Learning

arXiv 2605.19813 ↗First posted 19 May 2026cs.LG math.ST stat.THcited by 0

Not on the map. Why?

Abstract (arXiv)

Federated differentially private protocols can communicate over many adaptive rounds and reuse each client's local samples. Existing lower bound arguments for federated DP are often restricted to noninteractive protocols or fresh batch decompositions, so the fundamental information-theoretic limit of estimation under fully interactive protocols remains unknown. We establish a federated van Trees inequality for parameter estimation under squared ℓ2 loss from any complete public transcript satisfying a clientwise zCDP constraint at the sample level. A scalar trace form covers homogeneous experiments, while a matrix form preserves directional Fisher geometry in heterogeneous experiments where different clients are informative in different subspaces. Together with existing upper bounds for the corresponding problems, these results identify the minimax rates for various statistical problems including mean estimation, linear regression, nonparametric regression, and functional mean estimation over the full class of interactive public-transcript protocols. For these problems, arbitrary public interaction and repeated sample reuse do not improve the rate over simpler restricted protocols. The key technical ingredient in our paper is a contraction inequality for the Fisher information in the transcript: each client's contribution is bounded both by the Fisher information in its local experiment and by its total privacy budget.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 31 of its 46 references that are in the map. First posted on arXiv 19 May 2026.

Builds on

31 of 46 references.

References · 31

  1. 2016Concentrated Differential Privacy: Simplifications, Extensions, and Lower Boundscited by 339
  2. 2016Concentrated Differential Privacycited by 139
  3. 2014Differentially Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Boundscited by 104
  4. 2016Minimax Optimal Procedures for Locally Private Estimationcited by 103
  5. 2013Fingerprinting Codes and the Price of Approximate Differential Privacycited by 81
  6. 2020Differentially Private Assouad, Fano, and Le Camcited by 54
  7. 2022New Lower Bounds for Private Estimation and a Generalized Fingerprinting Lemmacited by 32
  8. 2021Private Federated Learning Without a Trusted Server: Optimal Algorithms for Convex Lossescited by 30
  9. 2013Local Privacy, Data Processing Inequalities, and Statistical Minimax Ratescited by 26
  10. 2023On the Privacy-Robustness-Utility Trilemma in Distributed Learningcited by 24
  11. 2020Fisher information under local differential privacycited by 22
  12. 2020Unified lower bounds for interactive high-dimensional estimation under information constraintscited by 22
19 more
  1. 2023Score Attack: A Lower Bound Technique for Optimal Differentially Private Learningcited by 21
  2. 2013Local Privacy and Minimax Bounds: Sharp Rates for Probability Estimationcited by 19
  3. 2022Discrete Distribution Estimation under User-level Local Differential Privacycited by 17
  4. 2019Local differential privacy: Elbow effect in optimal density estimation and adaptation over Besov ellipsoidscited by 13
  5. 2023Simple Binary Hypothesis Testing under Local Differential Privacy and Communication Constraintscited by 10
  6. 2023Smooth Lower Bounds for Differentially Private Algorithms via Padding-and-Permuting Fingerprinting Codescited by 8
  7. 2024Optimal Federated Learning for Nonparametric Regression with Heterogeneous Distributed Differential Privacy Constraintscited by 7
  8. 2024Federated Transfer Learning with Differential Privacycited by 6
  9. 2024Rate Optimality and Phase Transition for User-Level Local Differential Privacycited by 6
  10. 2024Federated Nonparametric Hypothesis Testing with Differential Privacy Constraints: Optimal Rates and Adaptive Testscited by 5
  11. 2023Improved Analysis of Sparse Linear Regression in Local Differential Privacy Modelcited by 4
  12. 2024Minimax And Adaptive Transfer Learning for Nonparametric Classification under Distributed Differential Privacy Constraintscited by 4
  13. 2024Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithmcited by 3
  14. 2024Optimal estimation in private distributed functional data analysiscited by 3
  15. 2024Differentially Private Federated Learning: Servers Trustworthiness, Estimation, and Statistical Inferencecited by 2
  16. 2024Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraintscited by 1
  17. 2025Nonparametric spectral density estimation using interactive mechanisms under local differential privacycited by 1
  18. 2025Optimal Cox regression under federated differential privacy: coefficients and cumulative hazardscited by 1
  19. 2026Minimax and Adaptive Covariance Matrix Estimation under Differential Privacycited by 1

Built on by

Not cited yet.