Privacy-Preserving Frank-Wolfe on Shuffle Model

作     者：Ling-jie ZHANG Shi-song WU Hai ZHANG 

作者机构：School of Mathematics Northwest University School of Mathematics and Information Science Baoji University of Arts and Sciences China Southern Power Grid Artificial Intelligence Technology Company Limited 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报(英文版))

年 卷 期：2024年第4期

页      面：887-907页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 081104[工学-模式识别与智能系统] 08[工学] 0839[工学-网络空间安全] 0835[工学-软件工程] 0811[工学-控制科学与工程] 081201[工学-计算机系统结构] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China (No. U1811461  12326615) 

摘      要：In this paper,we design the differentially private variants of the classical Frank-Wolfe algorithm with shuffle model in the optimization of machine *** weak assumptions and the generalized linear loss （GLL） structure,we propose a noisy Frank-Wolfe with shuffle model algorithm （NoisyFWS） and a noisy variance-reduced Frank-Wolfe with the shuffle model algorithm （NoisyVRFWS） by adding calibrated laplace noise under shuffling scheme in the?p（p∈[1,2]）-case,and study their privacy as well as utility guarantees for the H?lder smoothness *** particular,the privacy guarantees are mainly achieved by using advanced composition and privacy amplification by *** utility bounds of the Noisy FWS and NoisyVRFWS are analyzed and obtained the optimal excess population risks ■ and ■with gradient complexity ■ for ■.It turns out that the risk rates under shuffling scheme are a nearly-dimension independent rate,which is consistent with the previous work in some *** addition,there is a vital tradeoff between （α,L）-H?lder smoothness GLL and the gradient *** linear gradient complexity O（n） is showed by the parameter α=1.