  A recent algorithmic family for distributed optimization, DIGing's, have been
shown to have geometric convergence over time-varying undirected/directed
graphs. Nevertheless, an identical step-size for all agents is needed. In this
paper, we study the convergence rates of the Adapt-Then-Combine (ATC) variation
of the DIGing algorithm under uncoordinated step-sizes. We show that the ATC
variation of DIGing algorithm converges geometrically fast even if the
step-sizes are different among the agents. In addition, our analysis implies
that the ATC structure can accelerate convergence compared to the distributed
gradient descent (DGD) structure which has been used in the original DIGing
algorithm.

Optimization and Control;Systems and Control;Machine Learning