  This paper considers the problem of multi-agent distributed linear regression
in the presence of system noises. In this problem, the system comprises
multiple agents wherein each agent locally observes a set of data points, and
the agents' goal is to compute a linear model that best fits the collective
data points observed by all the agents. We consider a server-based distributed
architecture where the agents interact with a common server to solve the
problem; however, the server cannot access the agents' data points. We consider
a practical scenario wherein the system either has observation noise, i.e., the
data points observed by the agents are corrupted, or has process noise, i.e.,
the computations performed by the server and the agents are corrupted. In
noise-free systems, the recently proposed distributed linear regression
algorithm, named the Iteratively Pre-conditioned Gradient-descent (IPG) method,
has been claimed to converge faster than related methods. In this paper, we
study the robustness of the IPG method, against both the observation noise and
the process noise. We empirically show that the robustness of the IPG method
compares favorably to the state-of-the-art algorithms.
