Incremental Methods for Additive Cost Convex Optimization

Motivated by machine learning problems over large data sets and distributed optimization over networks, we consider the problem of minimizing the sum of a large number of convex component functions. We study incremental gradient methods for solving such problems, which use information about a single component function at each iteration. We provide new convergence rate results under some assumptions. We also consider incremental aggregated gradient methods, which compute a single component function gradient at each iteration while using outdated gradients of all component functions to approximate the entire global cost function, and provide new linear rate results.

This is joint work with Mert Gurbuzbalaban and Pablo Parrilo.