Byzantine-resilient Federated Low Rank Column-wise Compressive Sensing

In this work we consider the low rank column-wise (compressive) sensing (LRCCS) problem within a horizontally federated framework. We introduce a fast and communication-efficient algorithm for solving this problem, while being provably resilient to Byzantine attacks on all but the initial iterations of the algorithm. We do this by modifying our recently developed GD-based algorithm called AltGDmin (alternating GD and minimization) by replacing the summation/mean step of its GD step by the geometric median (GM).