We present a variational characterization for the R\'{e}nyi divergence of order infinity. Our characterization is related to guessing: the objective functional is a ratio of maximal expected values of a gain function applied to the probability of correctly guessing an unknown random variable. An important aspect of our variational characterization is that it remains agnostic to the particular gain function considered, as long as it satisfies some regularity conditions. Also, we define two variants of a tunable measure of information leakage, the maximal $\alpha$-leakage, and obtain closed-form expressions for these information measures by leveraging our variational characterization.

翻译：我们提出了R\'{{e}nyi 顺序无限性差异的变异定性。我们的定性与猜测有关:客观功能是收益函数最大预期值之比,用于正确猜测未知随机变量的概率。我们变异定性的一个重要方面是,只要满足某些常规性条件,它仍然对所考虑的特定收益函数具有不可知性。此外,我们定义了两种可以测量的信息渗漏量的变式,即最大值 $\alpha$-leakage,并通过利用我们的变异特性,为这些信息计量获取封闭式表达方式。