文献类型：期刊文献

中文题名：聚合博弈的差分隐私分布式算法:一种Frank-Wolfe方法

英文题名：Differential privacy in aggregative games:A distributed algorithm based on Frank-Wolfe method

作者：杨通清 莫立坡 龙飞 符义昊

第一作者：杨通清

机构：[1]北京工商大学数学与统计学院,北京100048;[2]北京物资学院系统科学研究院,北京101149;[3]贵州理工学院人工智能与电气工程学院,贵阳550025

第一机构：北京工商大学数学与统计学院,北京100048

年份：2025

卷号：40

期号：5

起止页码：1677-1686

中文期刊名：控制与决策

外文期刊名：Control and Decision

收录：;EI(收录号：20251618260107);北大核心:【北大核心2023】；

基金：国家自然科学基金项目(62473009)。

语种：中文

中文关键词：分布式博弈;差分隐私;聚合博弈;寻找纳什均衡;隐私保护;Frank-Wolfe方法

外文关键词：distributed game;differential privacy;aggregated game;Nash equilibrium seeking;privacy protection;Frank-Wolfe method

摘要：考虑聚合博弈的隐私保护分布式纳什均衡寻求算法设计.特别地,考虑该博弈不存在中心节点,在这种情况下,每个玩家无法直接获得用于策略更新所需的聚合策略信息,采用动态跟踪一致性协议对其进行估计,其中玩家用于估计聚合策略的状态量被认为是需要保护的敏感信息.为了保护玩家的隐私,利用相互独立的高斯噪声对玩家的梯度信息进行干扰.通过将Frank-Wolfe方法与动态跟踪一致性协议相结合,设计时变通信拓扑下带约束聚合博弈的分布式纳什均衡寻求算法.进而,分析算法实现-差分隐私的方差界.此外,通过对聚合项估计误差的收敛性分析得到算法收敛的充分条件,给出算法的收敛性证明.最后,通过数值仿真验证了所提出算法的有效性和收敛速度更快的优越性.(ε,δ)
This paper considers the design of a privacy-preserving distributed Nash equilibrium seeking algorithm for aggregated games.Specifically,we address scenarios where there is no central node,and in such cases,each player cannot directly obtain the aggregated strategy information required for strategy updates.In this paper,a dynamic tracking consensus protocol is employed to estimate this information.The state variables used by players to estimate the aggregated strategies are regarded as sensitive information that requires protection.To safeguard the players'privacy,independent Gaussian noise is used to perturb the players'gradient information.By combining the Frank-Wolfe method with the dynamic tracking consensus protocol,we design a distributed Nash equilibrium seeking algorithm for constrained aggregated games under time-varying communication topologies.Further,we analyze the variance bounds necessary for the algorithm to achieve(e,o)-differential privacy.Furthermore,by analyzing the convergence of the estimation error of the aggregated term,we derive sufficient conditions for the convergence of the algorithm and provide a proof of convergence.Finally,the effectiveness and superior convergence speed of the proposed algorithm are validated through numerical simulations.