Truncated Non-Uniform Quantization for Distributed SGD

To address the communication bottleneck challenge in distributed learning, our work introduces a novel two-stage quantization strategy designed to enhance the communication efficiency of distributed Stochastic Gradient Descent (SGD). The proposed method initially employs truncation to mitigate the impact of long-tail noise, followed by a non-uniform quantization of the post-truncation gradients based on their statistical characteristics. We provide a comprehensive convergence analysis of the quantized distributed SGD, establishing theoretical guarantees for its performance. Furthermore, by minimizing the convergence error, we derive optimal closed-form solutions for the truncation threshold and non-uniform quantization levels under given communication constraints. Both theoretical insights and extensive experimental evaluations demonstrate that our proposed algorithm outperforms existing quantization schemes, striking a superior balance between communication efficiency and convergence performance.