Summary of The Effectiveness Of Local Updates For Decentralized Learning Under Data Heterogeneity, by Tongle Wu et al.
The Effectiveness of Local Updates for Decentralized Learning under Data Heterogeneity
by Tongle Wu, Zhize Li, Ying Sun
First submitted to arxiv on: 23 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper revisits two fundamental decentralized optimization methods, Decentralized Gradient Tracking (DGT) and Decentralized Gradient Descent (DGD), with multiple local updates. The authors show that incorporating local update steps can reduce communication complexity for strongly convex and smooth loss functions. Specifically, they prove that local DGT achieves a communication complexity of O(L/μ(K+1)) + … where K is the number of additional local updates, ρ measures network connectivity, and δ measures second-order heterogeneity. The results reveal a tradeoff between communication and computation and show that increasing K can effectively reduce communication costs when data heterogeneity is low and the network is well-connected. The authors also consider the over-parameterization regime where local losses share the same minimums and prove that employing local updates in DGD achieves exact linear convergence under the Polyak-Łojasiewicz (PL) condition, which can yield a similar effect as DGT in reducing communication complexity. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at ways to make decentralized optimization more efficient. It shows how adding extra steps to two popular methods, Decentralized Gradient Tracking and Decentralized Gradient Descent, can reduce the amount of information that needs to be shared between devices. This is especially helpful when there’s a lot of data heterogeneity (i.e., different devices have different datasets) or network connectivity issues. The authors also explore how this approach works in cases where all devices are working with the same type of data and prove that it can lead to faster convergence. |
Keywords
* Artificial intelligence * Gradient descent * Optimization * Tracking
