Instance-Optimal Differentially Private Estimation
This work addresses the need for more efficient and adaptive private estimation methods in statistics, though it is incremental as it builds directly on existing private testing algorithms.
The paper tackles the problem of designing differentially private estimators that adapt to easy problem instances, achieving local minimax optimal convergence rates for one-parameter exponential families and tail rate estimation, by leveraging optimal private testers from prior work.
In this work, we study local minimax convergence estimation rates subject to $ε$-differential privacy. Unlike worst-case rates, which may be conservative, algorithms that are locally minimax optimal must adapt to easy instances of the problem. We construct locally minimax differentially private estimators for one-parameter exponential families and estimating the tail rate of a distribution. In these cases, we show that optimal algorithms for simple hypothesis testing, namely the recent optimal private testers of Canonne et al. (2019), directly inform the design of locally minimax estimation algorithms.