  Decentralized learning and optimization is a central problem in control that
encompasses several existing and emerging applications, such as federated
learning. While there exists a vast literature on this topic and most methods
centered around the celebrated average-consensus paradigm, less attention has
been devoted to scenarios where the communication between the agents may be
imperfect. To this end, this paper presents three different algorithms of
Decentralized Federated Learning (DFL) in the presence of imperfect information
sharing modeled as noisy communication channels. The first algorithm, Federated
Noisy Decentralized Learning (FedNDL1), comes from the literature, where the
noise is added to their parameters to simulate the scenario of the presence of
noisy communication channels. This algorithm shares parameters to form a
consensus with the clients based on a communication graph topology through a
noisy communication channel. The proposed second algorithm (FedNDL2) is similar
to the first algorithm but with added noise to the parameters, and it performs
the gossip averaging before the gradient optimization. The proposed third
algorithm
  (FedNDL3), on the other hand, shares the gradients through noisy
communication channels instead of the parameters. Theoretical and experimental
results demonstrate that under imperfect information sharing, the third scheme
that mixes gradients is more robust in the presence of a noisy channel compared
with the algorithms from the literature that mix the parameters.
