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 a comparable complexity result 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.

翻译：我们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包含光滑项与非光滑凸项的复合目标函数。针对该问题，我们提出两种单时间尺度算法：Prox-DASA与Prox-DASA-GT。这些算法在采用恒定批次大小（即$\mathcal{O}(1)$）的条件下，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（如双循环）或更强假设的情况下，即可达到可比的复杂度结果。大量数值实验验证了我们的理论发现，并展示了所提算法相较于现有方法的优越性。