Private Stochastic Optimization in the Presence of Outliers: Optimal Rates for (Non-Smooth) Convex Losses and Extension to Non-Convex Losses. (arXiv:2209.07403v2 [cs.LG] UPDATED)

We study differentially private (DP) stochastic optimization (SO) with data
containing outliers and loss functions that are (possibly) not Lipschitz
continuous. To date, the vast majority of work on DP SO assumes that the loss
is uniformly Lipschitz over data (i.e. stochastic gradients are uniformly
bounded over all data points). While this assumption is convenient, it is often
unrealistic: in many practical problems, the loss function may not be uniformly
Lipschitz. Even when the loss function is Lipschitz continuous, the …

extension losses non optimization