Privacy-Compatibility For General Utility Metrics

In this note, we present a complete characterization of the utility metrics that allow for non-trivial differential privacy guarantees.

💡 Research Summary

This paper addresses a fundamental question at the intersection of differential privacy (DP) and utility: which utility metrics can coexist with non‑trivial privacy guarantees? While the DP literature traditionally focuses on sensitivity analysis and the choice of noise distributions, the authors shift the focus to the metric that quantifies utility loss. They introduce the notion of privacy‑compatibility for a utility metric and provide a complete, mathematically rigorous characterization of the class of metrics that satisfy this property.

Problem Setting
Let (X) denote the space of databases and (Y) the output space. A statistical query is a deterministic function (f : X \to Y). To evaluate the quality of a randomized mechanism (M : X \to \Delta(Y)) (where (\Delta(Y)) is the set of probability distributions over (Y)), a distance function (d_Y : Y \times Y \to \mathbb{R}_{\ge 0}) is fixed. The expected utility loss is (\mathbb{E}