  This paper examines Federated learning (FL) in a Stochastic Approximation
(SA) framework. FL is a collaborative way to train neural network models across
various participants or clients without centralizing their data. Each client
will train a model on their respective data and send the weights across to a
the server periodically for aggregation. The server aggregates these weights
which are then used by the clients to re-initialize their neural network and
continue the training. SA is an iterative algorithm that uses approximate
sample gradients and tapering step size to locate a minimizer of a cost
function. In this paper the clients use a stochastic approximation iterate to
update the weights of its neural network. It is shown that the aggregated
weights track an autonomous ODE. Numerical simulations are performed and the
results are compared with standard algorithms like FedAvg and FedProx. It is
observed that the proposed algorithm is robust and gives more reliable
estimates of the weights, in particular when the clients data are not
identically distributed.
