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

arXiv:2605.19813v1 Announce Type: new 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.

Source: arXiv cs.LG | 2026-05-20