Information density and its exponential form, known as lift, play a central role in information privacy leakage measures. $\alpha$-lift is the power-mean of lift, which is tunable between the worst-case measure max-lift ($\alpha=\infty$) and more relaxed versions ($\alpha<\infty$). This paper investigates the optimization problem of the privacy-utility tradeoff where $\alpha$-lift and mutual information are privacy and utility measures, respectively. Due to the nonlinear nature of $\alpha$-lift for $\alpha<\infty$, finding the optimal solution is challenging. Therefore, we propose a heuristic algorithm to estimate the optimal utility for each value of $\alpha$, inspired by the optimal solution for $\alpha=\infty$. In proposing the algorithm, we prove and use the convexity of $\alpha$-lift with respect to the lift.

翻译：信息密度及其指数形式（称为提升度）在信息隐私泄露度量中具有核心作用。α-提升度是提升度的幂平均，可在最坏情况度量最大提升度（α=∞）与更宽松的版本（α<∞）之间调节。本文研究了以α-提升度作为隐私度量、互信息作为效用度量的隐私-效用权衡优化问题。由于α<∞时α-提升度的非线性特性，寻求最优解具有挑战性。为此，受α=∞最优解的启发，我们提出一种启发式算法来估计每个α值对应的最优效用。在算法构建过程中，我们证明并利用了α-提升度关于提升度的凸性。