Online Convex Optimization Over Erdos-Renyi Random Networks

The work studies how node-to-node communications over an Erd\H{o}s-R\'enyi random network influence distributed online convex optimization, which is vital in solving large-scale machine learning in antagonistic or changing environments. At per step, each node (computing unit) makes a local decision, experiences a loss evaluated with a convex function, and communicates the decision with other nodes over a network. The node-to-node communications are described by the Erd\H{o}s-R\'enyi rule, where independently each link takes place with a probability p over a prescribed connected graph. The objective is to minimize the system-wide loss accumulated over a finite time horizon. We consider standard distributed gradient descents with full gradients, one-point bandits and two-points bandits for convex and strongly convex losses, respectively.