  Federated Learning has been recently proposed for distributed model training
at the edge. The principle of this approach is to aggregate models learned on
distributed clients to obtain a new more general "average" model (FedAvg). The
resulting model is then redistributed to clients for further training. To date,
the most popular federated learning algorithm uses coordinate-wise averaging of
the model parameters for aggregation. In this paper, we carry out a complete
general mathematical convergence analysis to evaluate aggregation strategies in
a federated learning framework. From this, we derive novel aggregation
algorithms which are able to modify their model architecture by differentiating
client contributions according to the value of their losses. Moreover, we go
beyond the assumptions introduced in theory, by evaluating the performance of
these strategies and by comparing them with the one of FedAvg in classification
tasks in both the IID and the Non-IID framework without additional hypothesis.
