Decentralized learning on resource-constrained edge devices demands algorithms that are communication-efficient, robust to data corruption, and lightweight in memory. State-of-the-art gossip-based methods address communication efficiency, but achieving robustness remains challenging. Methods for robust estimation and optimization typically rely on non-smooth objectives (\textit{e.g.}, pinball loss, $\ell_1$ loss), yet standard gossip methods are primarily designed for smooth losses. Asynchronous decentralized ADMM-based methods have been proposed to handle such non-smooth objectives; however, existing approaches require memory that scales with node degree, making them impractical when memory is limited. We propose AsylADMM, a novel asynchronous gossip algorithm for decentralized non-smooth optimization requiring only two variables per node. We provide a new theoretical analysis for the synchronous variant and leverage it to prove convergence of AsylADMM in a simplified setting based on the squared loss. Empirically, AsylADMM converges faster than existing baselines on challenging non-smooth problems, including quantile and geometric median estimation, lasso regression, and robust regression. More broadly, our novel gossip framework opens a practical pathway toward robust and non-smooth decentralized learning.

翻译：摘要：在资源受限的边缘设备上进行去中心化学习，需要通信高效、对数据损坏具有鲁棒性且内存占用轻量的算法。最先进的高斯方法解决了通信效率问题，但实现鲁棒性仍然具有挑战性。用于鲁棒估计和优化的方法通常依赖于非光滑目标（例如，分位数损失、ℓ₁损失），而标准高斯方法主要针对光滑损失设计。已有异步去中心化ADMM方法被提出用于处理此类非光滑目标；然而，现有方法需要与节点度数成比例的内存，这在内存受限时不可行。我们提出AsylADMM，一种新颖的异步高斯算法，用于去中心化非光滑优化，每个节点仅需两个变量。我们为同步变体提供了新的理论分析，并利用它证明了AsylADMM在基于平方损失的简化设置下的收敛性。实验表明，AsylADMM在具有挑战性的非光滑问题上（包括分位数和几何中位数估计、套索回归和鲁棒回归）收敛速度快于现有基线。更广泛地说，我们新颖的高斯框架为鲁棒且非光滑的去中心化学习开辟了一条实用路径。