Fast Federated Low Rank Matrix Completion

For the low rank matrix completion problem, we develop a fast, communication-efficient and private algorithm, called Alternating Gradient Descent and Minimization (AltGDMin). The communication-efficiency and privacy claims assume a vertically federated setting in which each node observes some entries of a different subset of columns of the unknown LR matrix X*. By extensive simulation experiments, we demonstrate the superior communication efficiency of AltGDMin. We also numerically evaluate the sample complexity and show competitive performance compared to benchmark methods.