For efficient training, we seek to optimize an upper-bound of the objectiveresulting intwosimpleterms.

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.

Often, one needs to consider fairness for a large number of high-dimensional data points.