VarianceReduced

In recent centralized nonconvex distributed learning and federated learning, localmethods areoneofthepromising approaches toreducecommunication time. However, existing work has mainly focused on studying first-order optimality guarantees. On the other side, second-order optimality guaranteed algorithms, i.e., algorithms escaping saddle points, havebeen extensivelystudied inthenondistributed optimization literature.