Research On The Theory And Algorithm Of Non-convex Regularized Optimization For Differential Privacy Protectio

Differential privacy is a special privacy protection method.It has been widely used in many fields,such as displaying commuting patterns at the US Census Bureau,sharing historical traffic statistics on Google,etc.Therefore,differential privacy has become a hot research topic in optimization and related fields in recent years.In practical application,combined with the empirical risk minimization problem,the accuracy of data query results can be guaranteed and the privacy of user contributors can be protected from disclosure.The way to achieve differential privacy protection is to start from an algorithm that does not satisfy differential privacy,and appropriately add a certain distribution of noise to the algorithm to randomize the query results.This paper mainly studies the empirical risk minimization problem with non-convex regularization under privacy protection,and combines the iterative contraction threshold algorithm to add noise satisfying differential privacy to the gradient to get an algorithm satisfying privacy protection.The specific research content is as follows:(1)Aiming at the empirical risk minimization problem of MCP regularization,the design and implementation of differential privacy algorithm under gradient perturbation is studied.Based on the idea of Barzilar-Borwein(BB)method,an iterative shrinkage threshold algorithm based on BB step is proposed for line search.The algorithm does not involve any parameter selection in the process of BB step size determination,avoiding the difficulty of parameter tuning and the influence of parameter selection on the calculation effect.Secondly,it is proved that the algorithm has differential privacy protection property and convergence.(2)Based on two types of classical optimization problems in machine learning: Logistic regression(LR)problem and support vector machine(SVM)problem,random data satisfying Gaussian distribution and five-year Polish companies bankruptcy data were adopted to carry out a series of numerical simulation experiments.The validity of the proposed theory and algorithm is verified.In practical application,combined with the empirical risk minimization problem,the accuracy of data query results can be guaranteed and the privacy of user contributors can be protected from disclosure.