Near Instance-Optimality in Differential Privacy
Abstract
We develop two notions of instance optimality in differential privacy, inspired by classical statistical theory: one by defining a local minimax risk and the other by considering unbiased mechanisms and analogizing the Cramer-Rao bound, and we show that the local modulus of continuity of the estimand of interest completely determines these quantities. We also develop a complementary collection mechanisms, which we term the inverse sensitivity mechanisms, which are instance optimal (or nearly instance optimal) for a large class of estimands. Moreover, these mechanisms uniformly outperform the smooth sensitivity framework on each instance for several function classes of interest, including real-valued continuous functions. We carefully present two instantiations of the mechanisms for median and robust regression estimation with corresponding experiments.
Cite
@article{arxiv.2005.10630,
title = {Near Instance-Optimality in Differential Privacy},
author = {Hilal Asi and John C. Duchi},
journal= {arXiv preprint arXiv:2005.10630},
year = {2020}
}