Duff: A Dataset-Distance-Based Utility Function Family for the Exponential Mechanism
This work addresses the challenge of enhancing accuracy in differential privacy mechanisms for statisticians and data analysts, representing an incremental advance by providing a novel utility function that improves upon prior approaches.
The authors tackled the problem of improving fidelity in differentially private statistics by proposing Duff, a dataset-distance-based utility function family for the exponential mechanism, which offers provably higher fidelity compared to existing methods based on smooth sensitivity, as demonstrated in empirical evaluations for median computation.
We propose and analyze a general-purpose dataset-distance-based utility function family, Duff, for differential privacy's exponential mechanism. Given a particular dataset and a statistic (e.g., median, mode), this function family assigns utility to a possible output o based on the number of individuals whose data would have to be added to or removed from the dataset in order for the statistic to take on value o. We show that the exponential mechanism based on Duff often offers provably higher fidelity to the statistic's true value compared to existing differential privacy mechanisms based on smooth sensitivity. In particular, Duff is an affirmative answer to the open question of whether it is possible to have a noise distribution whose variance is proportional to smooth sensitivity and whose tails decay at a faster-than-polynomial rate. We conclude our paper with an empirical evaluation of the practical advantages of Duff for the task of computing medians.