Quantized Stochastic Primal-Dual Methods for Distributed Optimization under Relaxed Global Geometry
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 c...
| Authors | Susmit Sarkar, Abhinav Raghuvanshi, Kushal Chakrabarti et al. |
|---|---|
| Primary category | math.OC |
| Published | 9 June 2026 |
| Last updated at source | 9 June 2026 |
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