  We propose Federated Accelerated Stochastic Gradient Descent (FedAc), a
principled acceleration of Federated Averaging (FedAvg, also known as Local
SGD) for distributed optimization. FedAc is the first provable acceleration of
FedAvg that improves convergence speed and communication efficiency on various
types of convex functions. For example, for strongly convex and smooth
functions, when using $M$ workers, the previous state-of-the-art FedAvg
analysis can achieve a linear speedup in $M$ if given $M$ rounds of
synchronization, whereas FedAc only requires $M^{\frac{1}{3}}$ rounds.
Moreover, we prove stronger guarantees for FedAc when the objectives are
third-order smooth. Our technique is based on a potential-based perturbed
iterate analysis, a novel stability analysis of generalized accelerated SGD,
and a strategic tradeoff between acceleration and stability.
