This paper considers decentralized nonsmooth nonconvex optimization problem with Lipschitz continuous local functions. We propose an efficient stochastic first-order method with client sampling, achieving the $(δ,ε)$-Goldstein stationary point with the overall sample complexity of ${\mathcal O}(δ^{-1}ε^{-3})$, the computation rounds of ${\mathcal O}(δ^{-1}ε^{-3})$, and the communication rounds of ${\tilde{\mathcal O}}(γ^{-1/2}δ^{-1}ε^{-3})$, where $γ$ is the spectral gap of the mixing matrix for the network. Our results achieve the optimal sample complexity and the sharper communication complexity than existing methods. We also extend our ideas to zeroth-order optimization. Moreover, the numerical experiments show the empirical advantage of our methods.

翻译：本文研究具有Lipschitz连续局部函数的去中心化非光滑非凸优化问题。我们提出了一种高效的随机一阶方法，该方法采用客户端采样技术，能够达到$(δ,ε)$-Goldstein稳定点，其总体样本复杂度为${\mathcal O}(δ^{-1}ε^{-3})$，计算轮数为${\mathcal O}(δ^{-1}ε^{-3})$，通信轮数为${\tilde{\mathcal O}}(γ^{-1/2}δ^{-1}ε^{-3})$，其中$γ$为网络混合矩阵的谱间隙。与现有方法相比，我们的结果达到了最优的样本复杂度和更优的通信复杂度。我们还将该思想推广至零阶优化。此外，数值实验表明我们的方法具有经验优势。