  Fundamental limits and optimal mechanisms of privacy-preserving data release
that aim to minimize the privacy leakage under utility constraints of
non-specific tasks are investigated. While the private feature is typically
determined and known by the users who release their data, the specific task in
which the released data is utilized is usually unknown. To address the lack of
information of the specific task, utility constraints laid on a set of possible
tasks are considered. The mechanism protects the privacy while satisfying
utility of all possible tasks in the set. First, the single-letter
characterization of the rate-leakage-distortion region is derived.
Characterization of the minimum leakage under log-loss distortion and
unconstrained released rate turns out to be a non-convex problem. Second,
focusing on the case where the raw data consists of independent components, we
show that the above problem can be decomposed into multiple parallel privacy
funnel (PF) problems with different weightings. We explicitly derive the
solution to each PF problem when the private feature is a deterministic
function of a data component. The solution is characterized by a leakage-free
threshold, and the minimum leakage is zero while the utility constraint is
below the threshold. Finally, we show that the optimal weighting of each PF
problem can be found by solving a linear program (LP). A sufficient released
rate to achieve the minimum leakage is also derived. Numerical results are
shown to illustrate the robustness of our approach against the task
non-specificity. Our results can also be extended to the differential privacy
metric. We show that the problem with multiple constraints can also be
decomposed into multiple single-constraint problems. However, the solution to
each single-constraint problem remains open and can only be solved by numerical
methods.
