Yu Zhan, Ho Daniel W C, Yuan Deming, Liu Jie
IEEE Trans Cybern. 2023 Jun;53(6):3561-3573. doi: 10.1109/TCYB.2021.3127278. Epub 2023 May 17.
This article is concerned with the distributed stochastic multiagent-constrained optimization problem over a time-varying network with a class of communication noise. This article considers the problem in composite optimization setting, which is more general in the literature of noisy network optimization. It is noteworthy that the mainstream existing methods for noisy network optimization are Euclidean projection based. Based on the Bregman projection-based mirror descent scheme, we present a non-Euclidean method and investigate their convergence behavior. This method is the distributed stochastic composite mirror descent type method (DSCMD-N), which provides a more general algorithm framework. Some new error bounds for DSCMD-N are obtained. To the best of our knowledge, this is the first work to analyze and derive convergence rates of optimization algorithm in noisy network optimization. We also show that an optimal rate of O(1/√T) in nonsmooth convex optimization can be obtained for the proposed method under appropriate communication noise condition. Moveover, novel convergence results are comprehensively derived in expectation convergence, high probability convergence, and almost surely sense.
本文关注的是具有一类通信噪声的时变网络上的分布式随机多智能体约束优化问题。本文在复合优化设置下考虑该问题，这在有噪声网络优化文献中更为普遍。值得注意的是，现有的主流有噪声网络优化方法是基于欧几里得投影的。基于基于布雷格曼投影的镜像下降方案，我们提出了一种非欧几里得方法并研究其收敛行为。该方法是分布式随机复合镜像下降型方法（DSCMD-N），它提供了一个更通用的算法框架。获得了一些关于DSCMD-N的新误差界。据我们所知，这是第一项分析和推导有噪声网络优化中优化算法收敛速率的工作。我们还表明，在所提出的方法在适当的通信噪声条件下，在非光滑凸优化中可以获得(O(1 / \sqrt{T}))的最优速率。此外，在期望收敛、高概率收敛和几乎必然意义上全面推导了新颖的收敛结果。
