  Differentially private multiple testing procedures can protect the
information of individuals used in hypothesis tests while guaranteeing a small
fraction of false discoveries. In this paper, we propose a differentially
private adaptive FDR control method that can control the classic FDR metric
exactly at a user-specified level $\alpha$ with privacy guarantee, which is a
non-trivial improvement compared to the differentially private
Benjamini-Hochberg method proposed in Dwork et al. (2021). Our analysis is
based on two key insights: 1) a novel p-value transformation that preserves
both privacy and the mirror conservative property, and 2) a mirror peeling
algorithm that allows the construction of the filtration and application of the
optimal stopping technique. Numerical studies demonstrate that the proposed
DP-AdaPT performs better compared to the existing differentially private FDR
control methods. Compared to the non-private AdaPT, it incurs a small accuracy
loss but significantly reduces the computation cost.
