The theoretical results highlight atrade-offbetween localization ofthe statistical risk and convergence speed to the long-term risk target.

Several attempts have been made to explore local significant differences in the past years.

Our solution to this task is simple: we split the latent codez into many independent blocks, and regularize the generator so that each block affects only a particular part of the image.

In this document we provide additional details and experiments.

Most notably, we obtain the first dimension-independent generalization bounds formulti-pass SGD inthenonsmooth case. Inaddition, our bounds allow us to derive a new algorithm for differentially private nonsmooth stochastic convex optimization withoptimal excess population risk.