  This paper considers the multi-agent distributed linear least-squares
problem. The system comprises multiple agents, each agent with a locally
observed set of data points, and a common server with whom the agents can
interact. The agents' goal is to compute a linear model that best fits the
collective data points observed by all the agents. In the server-based
distributed settings, the server cannot access the data points held by the
agents. The recently proposed Iteratively Pre-conditioned Gradient-descent
(IPG) method has been shown to converge faster than other existing distributed
algorithms that solve this problem. In the IPG algorithm, the server and the
agents perform numerous iterative computations. Each of these iterations relies
on the entire batch of data points observed by the agents for updating the
current estimate of the solution. Here, we extend the idea of iterative
pre-conditioning to the stochastic settings, where the server updates the
estimate and the iterative pre-conditioning matrix based on a single randomly
selected data point at every iteration. We show that our proposed Iteratively
Pre-conditioned Stochastic Gradient-descent (IPSG) method converges linearly in
expectation to a proximity of the solution. Importantly, we empirically show
that the proposed IPSG method's convergence rate compares favorably to
prominent stochastic algorithms for solving the linear least-squares problem in
server-based networks.
