The Effectiveness of Local Updates for Decentralized Learning under Data Heterogeneity

• URL: http://arxiv.org/abs/2403.15654v2
• Date: Wed, 11 Sep 2024 05:11:33 GMT
• Title: The Effectiveness of Local Updates for Decentralized Learning under Data Heterogeneity
• Authors: Tongle Wu, Ying Sun,
• Abstract summary: We revisit two fundamental decentralized optimization methods, Decentralized Gradient Tracking (DGT) and Decentralized Gradient Descent (DGD) We demonstrate that incorporating $K > 1$ local update steps can reduce communication complexity.
• Score: 2.845817138242963
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We revisit two fundamental decentralized optimization methods, Decentralized Gradient Tracking (DGT) and Decentralized Gradient Descent (DGD), with multiple local updates. We consider two settings and demonstrate that incorporating $K > 1$ local update steps can reduce communication complexity. Specifically, for $\mu$-strongly convex and $L$-smooth loss functions, we proved that local DGT achieves communication complexity $\tilde{\mathcal{O}} \Big(\frac{L}{\mu K} + \frac{\delta}{\mu (1 - \rho)} + \frac{\rho }{(1 - \rho)^2} \cdot \frac{L+ \delta}{\mu}\Big)$, where $\rho$ measures the network connectivity and $\delta$ measures the second-order heterogeneity of the local loss. Our result reveals the tradeoff between communication and computation and shows increasing $K$ can effectively reduce communication costs when the data heterogeneity is low and the network is well-connected. We then consider the over-parameterization regime where the local losses share the same minimums, we proved that employing local updates in DGD, even without gradient correction, can yield a similar effect as DGT in reducing communication complexity. Numerical experiments validate our theoretical results.

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