  Federated learning is a prime candidate for distributed machine learning at
the network edge due to the low communication complexity and privacy protection
among other attractive properties. However, existing algorithms face issues
with slow convergence and/or robustness of performance due to the considerable
heterogeneity of data distribution, computation and communication capability at
the edge. In this work, we tackle both of these issues by focusing on the key
component of model aggregation in federated learning systems and studying
optimal algorithms to perform this task. Particularly, we propose a contextual
aggregation scheme that achieves the optimal context-dependent bound on loss
reduction in each round of optimization. The aforementioned context-dependent
bound is derived from the particular participating devices in that round and an
assumption on smoothness of the overall loss function. We show that this
aggregation leads to a definite reduction of loss function at every round.
Furthermore, we can integrate our aggregation with many existing algorithms to
obtain the contextual versions. Our experimental results demonstrate
significant improvements in convergence speed and robustness of the contextual
versions compared to the original algorithms. We also consider different
variants of the contextual aggregation and show robust performance even in the
most extreme settings.
