发表机构
University of Virginia（弗吉尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种通信高效的差分隐私分布式优化方法，通过局部更新和梯度跟踪扰动实现隐私保护，并证明收敛性与无限时域隐私保证。
AI 中文摘要
本文研究利用梯度跟踪进行隐私保护的分布式优化，在连续通信轮次之间进行一次无通信的局部更新。由于仅靠局部计算无法保护梯度信息，我们在通信迭代时对原始状态和梯度跟踪方向同时添加扰动，同时保持局部更新无噪声。我们建立了一个用于跟踪的聚合变量，刻画了在添加随机噪声情况下极限一致点的特征，并在特定参数条件下证明了均值收敛性。我们还建立了在仿射目标邻接关系和几何衰减拉普拉斯扰动下，完整通信记录的无限时域纯差分隐私保证。仿真结果展示了所提方法在给定隐私预算下在收敛性和优化精度方面的优势。
英文摘要
This paper studies privacy-preserving distributed optimization using gradient tracking with one communication-free local update between consecutive communication rounds. Since local computation alone does not protect gradient information, we perturb both the primal state and the gradient-tracking direction at communication iterations while keeping local updates noise-free. We establish an aggregate variable for tracking, characterize the limiting consensus point in the presence of added random noise, and prove convergence in mean under certain parameter conditions. We also establish infinite-horizon pure differential privacy for the complete communication transcript under an affine objective adjacency relation and geometrically decaying Laplace perturbations. Simulation results illustrate the advantages of the proposed method in terms of the convergence and optimization accuracy given a privacy budget.
