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 $O(1/\sqrt {T})$ 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.

中文翻译：

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具有一类通信噪声的时变网络分布式随机约束复合优化

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代理约束优化问题。本文考虑了复合优化设置中的问题，这在噪声网络优化的文献中更为普遍。值得注意的是，现有的主流噪声网络优化方法都是基于欧氏投影的。基于 Bregman 基于投影的镜像下降方案，我们提出了一种非欧几里德方法并研究了它们的收敛行为。这种方法就是分布式随机复合镜像下降法（DSCMD-N），它提供了一个更通用的算法框架。获得了一些新的 DSCMD-N 误差界限。据我们所知，这是第一项分析和推导优化算法在嘈杂网络优化中的收敛速度的工作。我们还表明，最佳比率 $O(1/\sqrt {T})$在适当的通信噪声条件下，可以为所提出的方法获得非光滑凸优化。此外，新颖的收敛结果是在期望收敛、高概率收敛和几乎肯定意义上综合推导出来的。