Lasse Vuursteen: Optimality Theory for Adaptive Federated Estimation under Differential Privacy

We have the pleasure to have Lasse Vursteen (Duke University) presenting his work on Optimality Theory for Adaptive Federated Estimation under Differential Privacy (via Teams).

Abstract: This talk addresses adaptive density estimation under differential privacy, where the regularity of the underlying density is unknown. In classical nonparametric statistics, adaptation to unknown smoothness can come without any cost — but it turns out differential privacy fundamentally changes this picture: When smoothness is unknown, fundamentally unavoidable penalties arise.

Matching upper and lower bounds are presented that precisely quantify the cost of adaptation under the federated differential privacy framework, which includes both central and local DP as special cases. Results are presented for both mean square error and pointwise risk, which exhibit differing phenomena and highlight the subtle interplay between privacy constraints and adaptation.

A novel adaptive estimator is introduced that achieves optimal rates and strictly improves on existing methods. The key is a carefully designed noise mechanism that enables one-shot adaptation while preserving privacy. The talk concludes with a more general framework for studying adaptation costs beyond smoothness — applicable to adaptation between arbitrary nonparametric function classes.