On Random Subset Generalization Error Bounds and the Stochastic Gradient Langevin Dynamics Algorithm

Abstract: In this work, we unify several expected generalization error bounds based on random subsets using the framework developed by Hellstr\"om and Durisi [1]. First, we recover the bounds based on the individual sample mutual information from Bu et al. [2] and on a random subset of the dataset from Negrea et al. [3]. Then, we introduce their new, analogous bounds in the randomized subsample setting from Steinke and Zakynthinou [4], and we identify some limitations of the framework. Finally, we extend the bounds from Haghifam et al. [5] for Langevin dynamics to stochastic gradient Langevin dynamics and we refine them for loss functions with potentially large gradient norms.