Escaping Saddle Points with Bias-Variance Reduced Local Perturbed SGD for Communication Efficient Nonconvex Distributed Learning. (arXiv:2202.06083v2 [cs.LG] UPDATED)

In recent centralized nonconvex distributed learning and federated learning,
local methods are one of the promising approaches to reduce communication 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, have been extensively studied in the
non-distributed optimization literature. In this paper, we study a new local
algorithm called Bias-Variance Reduced Local Perturbed SGD (BVR-L-PSGD), that
combines the existing bias-variance reduced gradient estimator with parameter …

arxiv bias bias-variance communication distributed learning variance