Stochastic Proximal Gradient Consensus Over Time-Varying Networks

We consider solving a convex, nonsmooth and stochastic optimization problem over a multi-agent network. Each agent has access to a local objective function and can communicate with its immediate neighbors only. We develop a dynamic stochastic proximal-gradient consensus (DySPGC) algorithm, featuring: i) it works for both the static and randomly time-varying networks; ii) it can deal with either the exact or the stochastic gradient information; iii) it has provable rate of convergence. Interestingly, the developed algorithm includes as special cases many existing (and seemingly unrelated) first-order algorithms for distributed optimization over static networks, such as the EXTRA (Shi et al 2014), the PG-EXTRA (Shi at 2015), the IC/IDC-ADMM (Chang et al 2014), and the DLM (Ling et al 2015). It is also closely related to the classical distributed gradient method.