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Propose-Test-Release (PTR) is a differential privacy framework that workswith local sensitivity of functions, instead of their global sensitivity. Thisframework is typically used for releasing robust statistics such as median ortrimmed mean in a differentially private manner. While PTR is a commonframework introduced over a decade ago, using it in applications such as robustSGD where we need many adaptive robust queries is challenging. This is mainlydue to the lack of Renyi Differential Privacy (RDP) analysis, an essentialingredient underlying the moments accountant approach for differentiallyprivate deep learning. In this work, we generalize the standard PTR and derivethe first RDP bound for it when the target function has bounded globalsensitivity. We show that our RDP bound for PTR yields tighter DP guaranteesthan the directly analyzed $(\eps, \delta)$-DP. We also derive thealgorithm-specific privacy amplification bound of PTR under subsampling. Weshow that our bound is much tighter than the general upper bound and close tothe lower bound. Our RDP bounds enable tighter privacy loss calculation for thecomposition of many adaptive runs of PTR. As an application of our analysis, weshow that PTR and our theoretical results can be used to design differentiallyprivate variants for byzantine robust training algorithms that use robuststatistics for gradients aggregation. We conduct experiments on the settings oflabel, feature, and gradient corruption across different datasets andarchitectures. We show that PTR-based private and robust training algorithmsignificantly improves the utility compared with the baseline.

Renyi Differential Privacy of Propose-Test-Release and Applications to Private and Robust Machine Learning