  Classical differential private DP-SGD implements individual clipping with
random subsampling, which forces a mini-batch SGD approach. We provide a
general differential private algorithmic framework that goes beyond DP-SGD and
allows any possible first order optimizers (e.g., classical SGD and momentum
based SGD approaches) in combination with batch clipping, which clips an
aggregate of computed gradients rather than summing clipped gradients (as is
done in individual clipping). The framework also admits sampling techniques
beyond random subsampling such as shuffling. Our DP analysis follows the $f$-DP
approach and introduces a new proof technique which allows us to derive simple
closed form expressions and to also analyse group privacy. In particular, for
$E$ epochs work and groups of size $g$, we show a $\sqrt{g E}$ DP dependency
for batch clipping with shuffling.
