  We study strongly convex distributed optimization problems where a set of
agents are interested in solving a separable optimization problem
collaboratively. In this paper, we propose and study a two time-scale
decentralized gradient descent algorithm for a broad class of lossy sharing of
information over time-varying graphs. One time-scale fades out the (lossy)
incoming information from neighboring agents, and one time-scale regulates the
local loss functions' gradients. For strongly convex loss functions, with a
proper choice of step-sizes, we show that the agents' estimates converge to the
global optimal state at a rate of $O(T^{-1/2})$. Another important contribution
of this work is to provide novel tools to deal with diminishing average weights
over time-varying graphs.
