General Lower Bounds for Differentially Private Federated Learning with Arbitrary Public-Transcript Interactions

2026-05-19

AI Summary

This work addresses the lack of theoretical understanding regarding fundamental limits of parameter estimation in differentially private federated learning under arbitrary public interaction patterns. Focusing on federated protocols satisfying client-level zero-concentrated differential privacy (zCDP), the paper establishes a privacy–information contraction inequality applicable to general interactive mechanisms, even with arbitrary rounds and sample reuse. It further introduces, for the first time, a federated version of the van Trees lower bound framework. By integrating tools from information theory, statistical decision theory, and public transcript modeling, the authors derive tight minimax lower bounds on estimation error for tasks including mean estimation, linear regression, and nonparametric regression, thereby uncovering the intrinsic trade-offs among privacy guarantees, communication complexity, and statistical accuracy.

Abstract

We prove a general lower bound for differentially private federated learning protocols with arbitrary public-transcript interactions. The protocol may use any number of adaptive rounds, and each client's local samples may be reused across rounds. For parameter estimation under squared \(\ell_2\) loss, we establish a federated van Trees lower bound for every estimator satisfying a total clientwise sample-level zero-concentrated differential privacy (zCDP) constraint. The main technical ingredient is a privacy-information contraction inequality for complete public transcripts. We illustrate the bound through applications to mean estimation, linear regression, and nonparametric regression.

Problem

• differentially private federated learning
• public-transcript interactions
• parameter estimation
• zero-concentrated differential privacy
• lower bounds

Innovation

• differentially private federated learning
• public-transcript interactions
• privacy-information contraction
• zero-concentrated differential privacy
• van Trees lower bound