Differentially Private Distributed Nonconvex Stochastic Optimization With Quantized Communication

作者：Jialong Chen, Jimin Wang, Ji‐Feng Zhang · 发表于：IEEE Transactions on Automatic Control · 年份：2025 · DOI：10.1109/tac.2025.3590872 · 被引用次数：3 · 研究领域：Distributed Control Multi-Agent Systems、Stochastic Gradient Optimization Techniques、Cooperative Communication and Network Coding

This paper proposes a novel distributed nonconvex stochastic optimization algorithm that can achieve privacy protection and convergence simultaneously while improving communication efficiency. Specifically, each node adds general privacy noises to its local state to avoid information leakage, and then, quantizes its noise-perturbed state before transmitting to improve communication efficiency. By using a sampling parameter-controlled subsampling method, the proposed algorithm enhances the differential privacy level compared to the existing works. By using a new convergence analysis technique, the mean square convergence for nonconvex cost functions is given without assuming that gradients are bounded. Furthermore, when the nonconvex cost function satisfies the Polyak-Łojasiewicz condition, a convergence rate and the oracle complexity of the proposed algorithm are given. By using a two-time-scale step-sizes method and a probabilistic quantizer, the proposed algorithm achieves finite cumulative differential privacy budgets$\epsilon$,$\delta$and the mean square convergence simultaneously while improving communication efficiency as the sample-size goes to infinity. A numerical example of the distributed training on the “MNIST” dataset is given to show the effectiveness and advantages of the algorithm.