Convex risk minimization is a commonly used setting in learning theory. In this paper, we firstly give a perturbation analysis for such algorithms, and then we apply this result to differential private learning algorithms. Our analysis needs the objective functions to be strongly convex. This leads to an extension of our previous analysis to the non-differentiable loss functions, when constructing differential private algorithms. Finally, an error analysis is then provided to show the selection for the parameters.
Weilin Nie and Cheng Wang carried out a perturbation analysis on the algorithm of convex risk minimization REF , and applied the analysis to the differential privacy learning algorithm.
Perturbation of convex risk minimization and its application in differential private learning algorithms