We focus on decentralized stochastic non-convex optimization, where $n$ agents work together to optimize a composite objective function which is a sum of a smooth term and a non-smooth convex term. To solve this problem, we propose two single-time scale algorithms: Prox-DASA and Prox-DASA-GT. These algorithms can find $\epsilon$-stationary points in $\mathcal{O}(n^{-1}\epsilon^{-2})$ iterations using constant batch sizes (i.e., $\mathcal{O}(1)$). Unlike prior work, our algorithms achieve comparable complexity without requiring large batch sizes, more complex per-iteration operations (such as double loops), or stronger assumptions. Our theoretical findings are supported by extensive numerical experiments, which demonstrate the superiority of our algorithms over previous approaches. Our code is available at https://github.com/xuxingc/ProxDASA.

翻译：本文聚焦于去中心化随机非凸优化问题，其中 $n$ 个智能体协同优化一个由光滑项和非光滑凸项组成的复合目标函数。为解决此问题，我们提出了两种单时间尺度算法：Prox-DASA 和 Prox-DASA-GT。这些算法在恒定批次大小（即 $\mathcal{O}(1)$）下，能够在 $\mathcal{O}(n^{-1}\epsilon^{-2})$ 次迭代内找到 $\epsilon$-稳定点。与先前工作不同，我们的算法在无需大批次大小、更复杂的每次迭代操作（如双重循环）或更强假设的条件下，实现了相当的计算复杂度。大量数值实验支持了我们的理论发现，证明了所提算法相较于先前方法的优越性。我们的代码可在 https://github.com/xuxingc/ProxDASA 获取。