Byzantine-Resilient Federated Alternating Gradient Descent and Minimization for Partly-Decoupled Low Rank Matrix Learning

This work has two contributions. First, we introduce novel provably Byzantine-resilient sampleand communication-efficient alternating gradient descent (GD) and minimization based algorithms for solving the federated low rank matrix completion (LRMC) problem. This involves learning a low rank (LR) matrix from a small subset of its entries. Second, we extend our ideas to show how a simple modification of our algorithms also provably solves two other partlydecoupled vertically federated LR matrix learning problem, -LR column-wise sensing (LRCS), also referred to as multi-task linear representation learning, and its phaseless generalization, LR phase retrieval (LRPR). In all problems, we consider column-wise or vertical federation, i.e. each node observes a small subset of entries of a disjoint column sub-matrix of the entire LR matrix.