  We present new methods for assessing the privacy guarantees of an algorithm
with regard to R\'enyi Differential Privacy. To the best of our knowledge, this
work is the first to address this problem in a black-box scenario, where only
algorithmic outputs are available. To quantify privacy leakage, we devise a new
estimator for the R\'enyi divergence of a pair of output distributions. This
estimator is transformed into a statistical lower bound that is proven to hold
for large samples with high probability. Our method is applicable for a broad
class of algorithms, including many well-known examples from the privacy
literature. We demonstrate the effectiveness of our approach by experiments
encompassing algorithms and privacy enhancing methods that have not been
considered in related works.
