  We present a class of methods for robust, personalized federated learning,
called Fed+, that unifies many federated learning algorithms. The principal
advantage of this class of methods is to better accommodate the real-world
characteristics found in federated training, such as the lack of IID data
across parties, the need for robustness to outliers or stragglers, and the
requirement to perform well on party-specific datasets. We achieve this through
a problem formulation that allows the central server to employ robust ways of
aggregating the local models while keeping the structure of local computation
intact. Without making any statistical assumption on the degree of
heterogeneity of local data across parties, we provide convergence guarantees
for Fed+ for convex and non-convex loss functions under different (robust)
aggregation methods. The Fed+ theory is also equipped to handle heterogeneous
computing environments including stragglers without additional assumptions;
specifically, the convergence results cover the general setting where the
number of local update steps across parties can vary. We demonstrate the
benefits of Fed+ through extensive experiments across standard benchmark
datasets.
