Escaping Saddle Points with Bias-Variance Reduced Local Perturbed SGD for Communication Efficient Nonconvex Distributed Learning

• URL: http://arxiv.org/abs/2202.06083v1
• Date: Sat, 12 Feb 2022 15:12:17 GMT
• Title: Escaping Saddle Points with Bias-Variance Reduced Local Perturbed SGD for Communication Efficient Nonconvex Distributed Learning
• Authors: Tomoya Murata and Taiji Suzuki
• Abstract summary: Local methods are one of the promising approaches to reduce communication time. We show that the communication complexity is better than non-local methods when the local datasets is smaller than the smoothness local loss.
• Score: 58.79085525115987
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 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 perturbation to find second-order optimal points in centralized nonconvex distributed optimization. BVR-L-PSGD enjoys second-order optimality with nearly the same communication complexity as the best known one of BVR-L-SGD to find first-order optimality. Particularly, the communication complexity is better than non-local methods when the local datasets heterogeneity is smaller than the smoothness of the local loss. In an extreme case, the communication complexity approaches to $\widetilde \Theta(1)$ when the local datasets heterogeneity goes to zero.

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