Distributed Stochastic Constrained Composite Optimization Over Time-Varying Network With a Class of Communication Noise
针对时变网络中存在通信噪声的分布式随机约束复合优化问题，提出基于Bregman投影的镜像下降方法，并证明在非光滑凸优化中可达到最优收敛速率O(1/√T)。
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.