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The Effectiveness of Local Updates for Decentralized Learning under Data Heterogeneity
March 26, 2024, 4:41 a.m. | Tongle Wu, Ying Sun
cs.LG updates on arXiv.org arxiv.org
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 …
abstract arxiv communication complexity cs.lg data decentralized gradient math.oc multiple optimization reduce tracking type update updates
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