Faster Convergence of Local SGD for Over-Parameterized Models

• URL: http://arxiv.org/abs/2201.12719v3
• Date: Mon, 10 Jun 2024 15:04:22 GMT
• Title: Faster Convergence of Local SGD for Over-Parameterized Models
• Authors: Tiancheng Qin, S. Rasoul Etesami, César A. Uribe,
• Abstract summary: Modern machine learning architectures are often highly expressive. We analyze the convergence of Local SGD (or FedAvg) for such over-parameterized functions in heterogeneous data setting. For general convex loss functions, we establish an error bound $O(K/T)$ otherwise. For non-loss functions, we prove an error bound $O(K/T)$ in both cases. We complete our results by providing problem instances in which our established convergence rates are tight to a constant factor with a reasonably small stepsize.
• Score: 1.5504102675587357
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Modern machine learning architectures are often highly expressive. They are usually over-parameterized and can interpolate the data by driving the empirical loss close to zero. We analyze the convergence of Local SGD (or FedAvg) for such over-parameterized models in the heterogeneous data setting and improve upon the existing literature by establishing the following convergence rates. For general convex loss functions, we establish an error bound of $\O(1/T)$ under a mild data similarity assumption and an error bound of $\O(K/T)$ otherwise, where $K$ is the number of local steps and $T$ is the total number of iterations. For non-convex loss functions we prove an error bound of $\O(K/T)$. These bounds improve upon the best previous bound of $\O(1/\sqrt{nT})$ in both cases, where $n$ is the number of nodes, when no assumption on the model being over-parameterized is made. We complete our results by providing problem instances in which our established convergence rates are tight to a constant factor with a reasonably small stepsize. Finally, we validate our theoretical results by performing large-scale numerical experiments that reveal the convergence behavior of Local SGD for practical over-parameterized deep learning models, in which the $\O(1/T)$ convergence rate of Local SGD is clearly shown.

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