title: Perturbation of convex risk minimization and its application in differential private learning algorithms.
abstract: 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.
authors.affiliation: Huizhou University, Huizhou, P.R. China.
authors.forename: Weilin
authors.initials: W
authors.lastname: Nie
authors.affiliation: Huizhou University, Huizhou, P.R. China.
authors.forename: Cheng
authors.initials: C
authors.lastname: Wang
keywords: concentration inequality; convex risk minimization; differential privacy; error decomposition; perturbation