Challenges of Differentially Private Release of Data Under an Open-world Assumption

Since its introduction a decade ago, differential privacy has been deployed and adapted in different application scenarios due to its rigorous protection of individuals' privacy regardless of the adversary's background knowledge. An urgent open research issue is how to query/release time evolving datasets in a differentially private manner. Most of the proposed solutions in this area focus on releasing private counters or histograms, which involve low sensitivity, and the main focus of these solutions is minimizing the amount of noise and the utility loss throughout the process. In this paper we consider the case of releasing private numerical values with unbounded sensitivity in a dataset that grows over time. While providing utility bounds for such case is of particular interest, we show that straightforward application of current mechanisms cannot guarantee (differential) privacy for individuals under an open-world assumption where data is continuously being updated, especially if the dataset is updated by an outlier.