Parallel SGD: When does averaging help?

Consider a number of workers running SGD independently on the same pool of data and averaging the models every once in a while — a common but not well understood practice. We study model averaging as a variance-reducing mechanism and describe two ways in which the frequency of averaging affects convergence. For convex objectives, we show the benefit of frequent averaging depends on the gradient variance envelope. For non-convex objectives, we illustrate that this benefit depends on the presence of multiple optimal points. We complement our findings with multicore experiments on both synthetic and real data.