Private Stochastic Optimization in the Presence of Outliers: Optimal Rates for (Non-Smooth) Convex Losses and Extension to Non-Convex Losses. (arXiv:2209.07403v1 [cs.LG])

We study differentially private (DP) stochastic optimization (SO) with data
containing outliers and loss functions that are not Lipschitz continuous. To
date, the vast majority of work on DP SO assumes that the loss is Lipschitz
(i.e. stochastic gradients are uniformly bounded), and their error bounds scale
with the Lipschitz parameter of the loss. While this assumption is convenient,
it is often unrealistic: in many practical problems where privacy is required,
data may contain outliers or be unbounded, causing some …

extension losses non optimization