Fast and Efficient Gossip Algorithms for Robust and Non-smooth Decentralized Learning
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909020809330688 |
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| author | van Elst, Anna Colin, Igor Clémençon, Stephan |
| author_facet | van Elst, Anna Colin, Igor Clémençon, Stephan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20571 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fast and Efficient Gossip Algorithms for Robust and Non-smooth Decentralized Learning van Elst, Anna Colin, Igor Clémençon, Stephan Machine Learning Artificial Intelligence 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. |
| title | Fast and Efficient Gossip Algorithms for Robust and Non-smooth Decentralized Learning |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2601.20571 |