Mirror Descent Based Database Privacy

In this paper, we focus on the problem of private database release in the interactive setting: a trusted database curator receives queries in an online manner for which it needs to respond with accurate but privacy preserving answers. To this end, we generalize the IDC (Iterative Database Construction) framework of [15,13] that maintains a differentially private artificial dataset and answers incoming linear queries using the artificial dataset. In particular, we formulate a generic IDC framework based on the Mirror Descent algorithm, a popular convex optimization algorithm [1]. We then present two concrete applications, namely, cut queries over a bipartite graph and linear queries over low-rank matrices, and provide significantly tighter error bounds than the ones by [15,13].