Dimension-Free Decentralized Nonsmooth Nonconvex Stochastic Optimization
We investigate decentralized nonsmooth nonconvex stochastic optimization over a network of $n$ nodes, with the goal of finding an $(δ,ε)$-Goldstein stationary point. The best existing algorithm achieves $O(δ^{-1}(ε^{-3}+dε^{-1}))$ sample complexity and $\widetilde{O}(γ^{-1/2}δ^{-1}(ε^{-3}+dε^{-1}))$ communication complexity, where $d$ is the problem dimension and $γ$ is the spectral gap of the communication matrix. However, the polynomial dependence on $d$ can be a major bottleneck in high-dimensional regimes. In this paper, we propose a novel algorithm that achieves $O(δ^{-1}ε^{-3})$ sample complexity and $\widetilde{O}(γ^{-1/2}δ^{-1}ε^{-3})$ communication complexity. The primary techniq...
| Authors | Yuanyu Wan, Lan Xue, Haomin Bai et al. |
|---|---|
| Primary category | math.OC |
| Published | 5 October 2026 |
| Last updated at source | 5 October 2026 |
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