This work develops a provably accurate fully-decentralized alternating projected gradient descent (GD) algorithm for recovering a low rank (LR) matrix from mutually independent projections of each of its columns, in a fast and communication-efficient fashion. To our best knowledge, this work is the first attempt to develop a provably correct decentralized algorithm (i) for any problem involving the use of an alternating projected GD algorithm; (ii) and for any problem in which the constraint set to be projected to is a non-convex set.

翻译：本文提出了一种可证明精确的全分散式交替投影梯度下降（GD）算法，用于从各列相互独立的投影中快速且通信高效地恢复低秩（LR）矩阵。据我们所知，本文是首个尝试开发可证明正确的分散式算法的工作，该算法（i）适用于任何涉及交替投影GD算法的问题；（ii）且适用于任何约束投影集为非凸集的问题。