General Lower Bounds for Differentially Private Federated Learning with Arbitrary Public-Transcript Interactions
Provides a fundamental theoretical limit for differentially private federated learning, which is important for understanding the trade-offs between privacy and accuracy in distributed settings.
This paper proves a general lower bound for differentially private federated learning protocols with arbitrary public-transcript interactions, establishing a federated van Trees bound for parameter estimation under squared ℓ2 loss with zCDP. The bound is applied to mean estimation, linear regression, and nonparametric regression.
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.