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We develop two new algorithms, called, FedDR and asyncFedDR, for solving afundamental nonconvex composite optimization problem in federated learning. Ouralgorithms rely on a novel combination between a nonconvex Douglas-Rachfordsplitting method, randomized block-coordinate strategies, and asynchronousimplementation. They can also handle convex regularizers. Unlike recent methodsin the literature, e.g., FedSplit and FedPD, our algorithms update only asubset of users at each communication round, and possibly in an asynchronousmanner, making them more practical. These new algorithms can handle statisticaland system heterogeneity, which are the two main challenges in federatedlearning, while achieving the best known communication complexity. In fact, ournew algorithms match the communication complexity lower bound up to a constantfactor under standard assumptions. Our numerical experiments illustrate theadvantages of our methods over existing algorithms on synthetic and realdatasets.

FedDR -- Randomized Douglas-Rachford Splitting Algorithms for Nonconvex Federated Composite Optimization