Abstract
Matrix-stepsized gradient descent algorithms have been demonstrated to exhibit superior efficiency in non-convex optimization compared to their scalar counterparts. The det-CGD algorithm, as introduced by Li et al. (2023), leverages matrix stepsizes to perform compressed gradient descent for non-convex objectives and matrix-smooth problems in a federated manner. The authors establish the algorithm’s convergence to a neighborhood of the weighted stationarity point under a convex condition for the symmetric and positive-definite stepsize matrix. In this paper, we propose a variance-reduced version of the det-CGD algorithm, incorporating the MARINA method. Notably, we establish theoretically and empirically, that det-MARINA outperforms both MARINA and the distributed det-CGD algorithms in terms of iteration and communication complexities.
