From Privacy to Generalization: Linear Max-Information Bounds for Differentially Private Learning Algorithms
This work establishes explicit finite-sample bounds for Differentially Private Stochastic Gradient Descent (DP-SGD), proving that its approximate max-information is $O E n ar{eta}^2 ar{ u} ( ext{log } E/ar{eta})$. This result allows constructing data-dependent priors for PAC-Bayes generalization bounds, providing a new bound controlled entirely by DP-SGD hyperparameters.