Comparing approximate and probabilistic differential privacy parameters

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. •Comparison of approximate and probabilistic differential privacy.•Analysis of how penalties on privacy parameters effect comparison.•Fixing either parameter gives a failure of one implication.•With sufficient penalties on both parameters, implication holds.