Instance-optimal Clipping for Summation Problems in the Shuffle Model of Differential Privacy

arXiv:2403.10116v1 Announce Type: new
Abstract: Differentially private mechanisms achieving worst-case optimal error bounds (e.g., the classical Laplace mechanism) are well-studied in the literature. However, when typical data are far from the worst case, \emph{instance-specific} error bounds -- which depend on the largest value in the dataset -- are more meaningful. For example, consider the sum estimation problem, where each user has an integer $x_i$ from the domain $\{0,1,\dots,U\}$ and we wish to estimate $\sum_i x_i$. This has a worst-case optimal …

arxiv case cs.cr cs.ds data dataset differential privacy error far instance literature mechanism privacy private problems shuffle value