Title: Private Top-$k$ Selection under Gumbel Differential Privacy Guarantees
Primary area: alignment, fairness, safety, privacy, and societal considerations
Keywords: Differential privacy, $f$-differential privacy, Gumbel mechanism, top-$k$ selection.

Abstract: From the perspective of hypothesis testing, $f$-differential privacy ($f$-DP) as a relaxation of differential privacy (DP) possesses numerous desirable properties, the most prominent of which is its lossless characterization of the composition of DP mechanisms.  Within the $f$-DP class, Gaussian differential privacy (GDP), as a canonical family introduced to design Gaussian mechanism, has  gained widespread acceptance. However, Gaussian mechanism is not the optimal option for all scenarios to ensure DP. As a type of extreme value distribution, Gumbel distribution is naturally considered to design private top-$k$ selection algorithms. In this work, a new family in $f$-DPs, named Gumbel differential privacy (GumDP), is developed to parameterize Gumbel mechanism as similar to GDP. And the composition of Gumbel mechanisms is studied. In addition, two important composition properties of the Gumbel mechanism are discovered among different private selection problems. Utilizing these, a novel privacy-preserving top-$k$ selection algorithm with Gumbel mechanism, called the peeling algorithm under oneshot RNM, is presented based on the Report Noisy Min (RNM) and peeling algorithms. Simulations demonstrate that the privacy-utility performance of the proposed private selection algorithm is significantly improved compared to the peeling algorithm under RNM with Laplace or Gaussian mechanism.

TL;DR: A novel privacy-preserving top-k selection algorithm under $f$-differential privacy is proposed based on the Gumbel distribution.