Better than Composition: How to Answer Multiple Relational Queries under Differential Privacy

Answering relational queries under differential privacy has attracted a lot of attention in recent years due to growing concerns on personal privacy, and instance-optimal mechanisms have been developed for a single query. However, most real-world data analytical tasks require multiple queries to be answered under a total privacy budget. The standard solution to extend the single-query mechanism to multiple queries is via privacy composition. However, we observe that this may yield an error bound that could be a d0.5-factor worse from the optimal, where d is the number of queries. In this paper, we present a different, more holistic approach that closes this gap. In addition to theoretical optimality, our new mechanism also significantly outperforms privacy composition in practice, especially on more skewed data and large d.