  Gradient-type distributed optimization methods have blossomed into one of the
most important tools for solving a minimization learning task over a networked
agent system. However, only one gradient update per iteration is difficult to
achieve a substantive acceleration of convergence. In this paper, we propose an
accelerated framework named as MUSIC allowing each agent to perform multiple
local updates and a single combination in each iteration. More importantly, we
equip inexact and exact distributed optimization methods into this framework,
thereby developing two new algorithms that exhibit accelerated linear
convergence and high communication efficiency. Our rigorous convergence
analysis reveals the sources of steady-state errors arising from inexact
policies and offers effective solutions. Numerical results based on synthetic
and real datasets demonstrate both our theoretical motivations and analysis, as
well as performance advantages.
