提出量化随机对偶方法，实现分布式优化的高效通信与稳定收敛。
Quantized Stochastic Primal-Dual Methods for Distributed Optimization under Relaxed Global Geometry
- 设计量化随机对偶算法，在有限比特通信下保持精度。
- 在非严格凸条件下实现线性收敛至噪声与量化误差决定的邻域。
- 适用于低带宽网络环境，适合资源受限的分布式系统部署。
我们研究在随机梯度与有限比特通信（由随机无偏量化建模）下的分布式优化问题。提出 q-PDGD——一种量化随机原始-对偶方法，并在弱全局几何条件下进行分析。在受限割线不等式（RSI）下，固定步长可实现线性收缩至由梯度噪声、量化失真和网络连通性决定的显式邻域；衰减步长可实现无需共享最小值假设的 O(1/k) 收敛。在 Polyak-Lojasiewicz (PL) 不等式下，同样获得线性到邻域的收敛。结果在最优查询复杂度上达到目前已知集中式随机方法的最佳水平，实验验证了量化级别、步长选择与图结构之间的预期权衡。
原文摘要 · Abstract (English)
We study distributed optimization with stochastic gradients and finite-bit communication modeled by random (unbiased) quantization. We propose q-PDGD, a quantized stochastic primal-dual method, and analyze it under relaxed global geometry. Under restricted secant inequality (RSI), a constant step-size yields linear contraction to an explicit neighborhood determined by gradient noise, quantization distortion, and network connectivity, while a diminishing step-size achieves O(1/k) convergence without shared-minimizer assumptions. Under Polyak-Lojasiewicz (PL) inequality, we obtain linear-to-neighborhood convergence in the same stochastic quantized setting. Our results match the best-known centralized stochastic rates in oracle complexity, and are supported by experiments demonstrating the predicted tradeoffs between quantization level, step-size choice, and graph structure.
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