  Federated learning (FL) is a distributed learning approach where a set of
end-user devices participate in the learning process by acting on their
isolated local data sets. Here, we process local data sets of users where
worst-case optimization theory is used to reformulate the FL problem where the
impact of local data sets in training phase is considered as an uncertain
function bounded in a closed uncertainty region. This representation allows us
to compare the performance of FL with its centralized counterpart, and to
replace the uncertain function with a concept of protection functions leading
to more tractable formulation. The latter supports applying a regularization
factor in each user cost function in FL to reach a better performance. We
evaluated our model using the MNIST data set versus the protection function
parameters, e.g., regularization factors.
