  Federated learning involves a central processor that works with multiple
agents to find a global model. The process consists of repeatedly exchanging
estimates, which results in the diffusion of information pertaining to the
local private data. Such a scheme can be inconvenient when dealing with
sensitive data, and therefore, there is a need for the privatization of the
algorithms. Furthermore, the current architecture of a server connected to
multiple clients is highly sensitive to communication failures and
computational overloads at the server. Thus in this work, we develop a private
multi-server federated learning scheme, which we call graph federated learning.
We use cryptographic and differential privacy concepts to privatize the
federated learning algorithm that we extend to the graph structure. We study
the effect of privatization on the performance of the learning algorithm for
general private schemes that can be modeled as additive noise. We show under
convexity and Lipschitz conditions, that the privatized process matches the
performance of the non-private algorithm, even when we increase the noise
variance.
