Security concerns in large-scale networked environments are becoming increasingly critical. To further improve the algorithm security from the design perspective of decentralized optimization algorithms, we introduce a new measure: Privacy Leakage Frequency (PLF), which reveals the relationship between communication and privacy leakage of algorithms, showing that lower PLF corresponds to lower privacy budgets. Based on such assertion, a novel differentially private decentralized primal--dual algorithm named DP-RECAL is proposed to take advantage of operator splitting method and relay communication mechanism to experience less PLF so as to reduce the overall privacy budget. To the best of our knowledge, compared with existing differentially private algorithms, DP-RECAL presents superior privacy performance and communication complexity. In addition, with uncoordinated network-independent stepsizes, we prove the convergence of DP-RECAL for general convex problems and establish a linear convergence rate under the metric subregularity. Evaluation analysis on least squares problem and numerical experiments on real-world datasets verify our theoretical results and demonstrate that DP-RECAL can defend some classical gradient leakage attacks.

翻译：大规模网络环境中的安全问题日益严峻。为从去中心化优化算法设计角度进一步提升算法安全性，本文提出隐私泄露频率（PLF）这一新度量，揭示了算法通信与隐私泄露之间的关联规律，表明较低的PLF对应更小的隐私预算。基于该论断，本文提出新型差分隐私去中心化原始-对偶算法DP-RECAL，该算法利用算子分裂方法与中继通信机制降低PLF，从而减少总体隐私预算。据我们所知，与现有差分隐私算法相比，DP-RECAL在隐私保护性能与通信复杂度方面均表现更优。此外，在非协调的网络无关步长设置下，我们证明了DP-RECAL对一般凸问题的收敛性，并在度量次正则条件下建立了线性收敛速率。针对最小二乘问题的评估分析与真实数据集的数值实验验证了理论结果，表明DP-RECAL能够有效防御典型的梯度泄露攻击。