Comparing approximate and probabilistic differential privacy parameters

Abstract

This paper compares two notions of differential privacy: approximate differential privacy (ADP) and probabilistic differential privacy (PrDP). It is well-known that the PrDP implies the ADP; and it was established in [7] that the ADP implies the PrDP, after a penalty on the parameters ε and δ that are used in the definitions of both properties. We show that the condition found in [7] is tight: if it fails, we construct a randomized algorithm that has ADP but not PrDP.