Differentially Private Gradient-Tracking-Based Distributed Stochastic Optimization Over Directed Graphs

• 成果类型: Article
• 署名作者: Chen, Jialong; Wang, Jimin; Zhang, Ji-Feng
• 署名单位: Chinese Academy of Sciences; Nanjing Institute of Geology & Paleontology, CAS; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; University of Science & Technology Beijing; Zhongyuan University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2026.3678834
• 发表日期: 2026

摘要

This article proposes a differentially private gradient-tracking-based distributed stochastic optimization algorithm over directed graphs. In particular, privacy noises are incorporated into each agent's state and tracking variable to mitigate information leakage, after which the perturbed states and tracking variables are transmitted to neighbors. We design two novel schemes for the step-sizes and the sampling number within the algorithm. The sampling parameter-controlled subsampling method employed by both schemes enhances the differential privacy level and ensures a finite cumulative privacy budget even over infinite iterations. The algorithm achieves both almost sure and mean square convergence for nonconvex objectives. Furthermore, when nonconvex objectives satisfy the Polyak-Lojasiewicz condition, Scheme (S1) achieves a polynomial mean square convergence rate, and Scheme (S2) achieves an exponential mean square convergence rate. The tradeoff between privacy and convergence is presented. The effectiveness of the algorithm and its superior performance compared to existing works are illustrated through numerical examples of distributed training on the benchmark datasets MNIST and CIFAR-10.