A Van Trees Lower Bound for Fully Interactive Differentially Private Federated Learning
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 \ell_2 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 ...
| Authors | T. Tony Cai, Yicheng Li |
|---|---|
| Primary category | cs.LG |
| Published | 19 May 2026 |
| Last updated at source | 8 July 2026 |
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