论文标题
通过一类通信噪声，分布式随机约束的复合优化在时间变化的网络上
Distributed Stochastic Constrained Composite Optimization over Time-Varying Network with a Class of Communication Noise
论文作者
论文摘要
本文涉及通过一类通信噪声在随着时间变化的网络上通过分布式随机多代理的约束优化问题。本文考虑了综合优化设置中的问题，在嘈杂网络优化的文献中更笼统。值得注意的是，嘈杂网络优化的现有现有方法是基于欧几里得投射的。基于Bregman投射基于镜的下降方案，我们提出了一种非欧对年人方法，并研究了它们的收敛行为。此方法是分布式随机复合镜下降类型方法（DSCMD-N），该方法提供了更通用的算法框架。获得了DSCMD-N的一些新误差界。 据我们所知，这是在嘈杂网络优化中分析和得出优化算法的收敛速率的第一项工作。我们还表明，在适当的通信噪声条件下，可以为提出的方法获得非平滑凸优化的$ O（1/\ sqrt {t}）$的最佳速率。此外，新颖的收敛结果在预期收敛，高概率收敛性以及几乎肯定的感觉中得到了全面得出。
This paper is concerned with distributed stochastic multi-agent constrained optimization problem over time-varying network with a class of communication noise. This paper 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 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. Moreover, novel convergence results are comprehensively derived in expectation convergence, high probability convergence, and almost surely sense.
