Privacy under hard distortion constraints

We study the problem of data disclosure with privacy guarantees, wherein the utility of the disclosed data is ensured via a hard distortion constraint. Unlike average distortion, hard distortion provides a deterministic guarantee of fidelity. For the privacy measure, we use a tunable information leakage measure, namely maximal α-leakage (α ∈ [1, ∞]), and formulate the privacy-utility tradeoff problem. The resulting solution highlights that under a hard distortion constraint, the nature of the solution remains unchanged for both local and non-local privacy requirements. More precisely, we show that both the optimal mechanism and the optimal tradeoff are invariant for any α > 1; i.e., the tunable leakage measure only behaves as either of the two extrema, i.e., mutual information for α = 1 and maximal leakage for α = ∞.