Differential Privacy Dynamics of Langevin Diffusion and Noisy Gradient Descent
This work addresses privacy concerns in machine learning for researchers and practitioners using iterative algorithms, offering a more accurate privacy analysis than previous methods, though it is incremental in refining existing differential privacy frameworks.
The paper tackles the problem of quantifying information leakage in iterative randomized learning algorithms, specifically for noisy gradient descent, by modeling the dynamics of Rényi differential privacy loss throughout training. It proves a tight bound on privacy loss that converges exponentially fast for smooth and strongly convex loss functions, improving over composition theorems, and achieves optimal utility with small gradient complexity for Lipschitz, smooth, and strongly convex functions.
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 Rényi differential privacy loss throughout the training process. Our analysis traces a provably \emph{tight} bound on the Rényi 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.