Randomized Block Proximal Methods for Distributed Stochastic Big-Data Optimization

In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. the addressed set-up, dimension decision variable can be extremely high and objective function nonsmooth. The general algorithm consists two main steps: consensus step an update on single block variable, which is then broadcast to neighbors. Three special instances proposed method, involving particular problem structures, are presented. case, convergence dynamic random row matrices shown. Then, optimal cost proven in expected value. Exact achieved when using diminishing (local) stepsizes, while approximate attained constant stepsizes employed. rate shown sublinear explicit provided case stepsizes. Finally, tested classification problem, first synthetic data and, then, real, high-dimensional, text dataset.