  We present a new method that includes three key components of distributed
optimization and federated learning: variance reduction of stochastic
gradients, partial participation, and compressed communication. We prove that
the new method has optimal oracle complexity and state-of-the-art communication
complexity in the partial participation setting. Regardless of the
communication compression feature, our method successfully combines variance
reduction and partial participation: we get the optimal oracle complexity,
never need the participation of all nodes, and do not require the bounded
gradients (dissimilarity) assumption.
