SILVER: Single-loop variance reduction and application to federated learning
Kazusato Oko, Shunta Akiyama, Denny Wu, Tomoya Murata, Taiji Suzuki
Most variance reduction methods require multiple times of full gradient computation, which is time-consuming and hence a bottleneck in application to distributed optimization. We present a single-loop variance-reduced gradient estimator named SILVER (SIngle-Loop VariancE-Reduction) for the finite-sum non-convex optimization, which does not require multiple full gradients but nevertheless achieves the optimal gradient complexity. Notably, unlike existing methods, SILVER provably reaches second-order optimality, with exponential convergence in the Polyak-Łojasiewicz (PL) region, and achieves further speedup depending on the data heterogeneity. Owing to these advantages, SILVER serves as a new base method to design communication-efficient federated learning algorithms: we combine SILVER with local updates which gives the best communication rounds and number of communicated gradients across all range of Hessian heterogeneity, and, at the same time, guarantees second-order optimality and exponential convergence in the PL region.
