Differential Privacy Dynamics of Langevin Diffusion and Noisy Gradient DescentDownload PDF

21 May 2021, 20:51 (modified: 26 Oct 2021, 15:48)NeurIPS 2021 SpotlightReaders: Everyone
Keywords: Differential Privacy, Noisy Gradient Descent
TL;DR: Tight converging differential privacy analysis for noisy gradient descent when only last iterate model is released.
Abstract: What is the information leakage of an iterative randomized learning algorithm about its training data, when the internal state of the algorithm is \emph{private}? How much is the contribution of each specific training epoch to the information leakage through the released model? We study this problem for noisy gradient descent algorithms, and model the \emph{dynamics} of R\'enyi differential privacy loss throughout the training process. Our analysis traces a provably \emph{tight} bound on the R\'enyi divergence between the pair of probability distributions over parameters of models trained on neighboring datasets. We prove that the privacy loss converges exponentially fast, for smooth and strongly convex loss functions, which is a significant improvement over composition theorems (which over-estimate the privacy loss by upper-bounding its total value over all intermediate gradient computations). For Lipschitz, smooth, and strongly convex loss functions, we prove optimal utility with a small gradient complexity for noisy gradient descent algorithms.
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