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We present new methods for assessing the privacy guarantees of an algorithmwith regard to R\'enyi Differential Privacy. To the best of our knowledge, thiswork is the first to address this problem in a black-box scenario, where onlyalgorithmic outputs are available. To quantify privacy leakage, we devise a newestimator for the R\'enyi divergence of a pair of output distributions. Thisestimator is transformed into a statistical lower bound that is proven to holdfor large samples with high probability. Our method is applicable for a broadclass of algorithms, including many well-known examples from the privacyliterature. We demonstrate the effectiveness of our approach by experimentsencompassing algorithms and privacy enhancing methods that have not beenconsidered in related works.

Lower Bounds for R\'enyi Differential Privacy in a Black-Box Setting