Clipped Decentralized SGD: Achieving Optimal Convergence and Linear Speed-Up Under Heavy-Tailed Noise
去中心化 SGD 克服重尾雜訊：梯度裁剪如何實現最佳收斂與線性加速
Heavy-tailed noise frequently destabilizes decentralized training. While gradient normalization often fails to converge without local momentum, this work shows that clipped DSGD achieves order-optimal convergence rates under bounded p-th moment noise (where p is between 1 and 2). By providing a sharp analysis of the consensus gap, the authors establish a linear speed-up relative to the number of agents—a theoretical breakthrough for decentralized clipping methods.
Key points
Order-Optimal Convergence
Clipped DSGD achieves order-optimal convergence rates both in expectation and with high probability under heavy-tailed noise.
Linear Speed-Up
Establishes a linear speed-up in the number of agents, which was previously unproven for decentralized methods using gradient clipping.
Consensus Gap Analysis
Exploits the mathematical structure of clipping to relegate network consensus errors to higher-order terms.
Clipping vs. Normalization
Unlike normalization which can fail to converge, clipping retains essential magnitude information, ensuring stability.
How it works
| 梯度裁剪 (Clipped DSGD) | 梯度正規化 (Normalized DSGD) | |
|---|---|---|
| Convergence Guarantee | 達到最優收斂率 (Order-optimal) | 在無本地動量時可能無法收斂 (May fail) |
| Magnitude Information | 保留梯度幅度資訊 (Retained) | 完全丟失梯度幅度資訊 (Lost) |
| Linear Speed-up | 證實可隨節點數增加而線性加速 | 需要額外機制（如本地動量或大批次） |
Why it matters
In edge computing and federated learning, heavy-tailed data noise often causes standard algorithms to fail. This work provides a rigorous theoretical foundation showing that simple gradient clipping enables decentralized systems to remain highly robust against extreme noise while scaling training speed linearly with the number of devices, bypassing the need for a central coordinator.
Who it affects
- AI Researcher
- AI Developer
- Student & Learner
How to use it
- 1Decentralized collaborative training across noisy edge devices and IoT sensors
- 2Robust optimization in Federated Learning against data outliers and impulsive noise
Limitations & caveats
- The analysis is restricted to smooth non-convex objective functions, leaving non-smooth settings unexplored.
- Assumes bounded p-th moment noise (p between 1 and 2), which may not cover extremely heavy-tailed noise beyond this range.
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