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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.14488 |
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| _version_ | 1866914044438380544 |
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| author | Lin, Ying Kuang, Yao Alacaoglu, Ahmet Friedlander, Michael P. |
| author_facet | Lin, Ying Kuang, Yao Alacaoglu, Ahmet Friedlander, Michael P. |
| contents | Distributed optimization requires nodes to coordinate, yet full synchronization scales poorly. When $n$ nodes collaborate through $m$ pairwise regularizers, standard methods demand $\mathcal{O}(m)$ communications per iteration. This paper proposes randomized local coordination: each node independently samples one regularizer uniformly and coordinates only with nodes sharing that term. This exploits partial separability, where each regularizer $G_j$ depends on a subset $S_j \subseteq \{1,\ldots,n\}$ of nodes. For graph-guided regularizers where $|S_j|=2$, expected communication drops to exactly 2 messages per iteration. This method achieves $\tilde{\mathcal{O}}(\varepsilon^{-2})$ iterations for convex objectives and under strong convexity, $\mathcal{O}(\varepsilon^{-1})$ to an $\varepsilon$-solution and $\mathcal{O}(\log(1/\varepsilon))$ to a neighborhood. Replacing the proximal map of the sum $\sum_j G_j$ with the proximal map of a single randomly selected regularizer $G_j$ preserves convergence while eliminating global coordination. Experiments validate both convergence rates and communication efficiency across synthetic and real-world datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decentralized Optimization with Topology-Independent Communication Lin, Ying Kuang, Yao Alacaoglu, Ahmet Friedlander, Michael P. Machine Learning Optimization and Control 90C25, 68T05 G.1.6; C.2.4; I.2.6; F.2.1 Distributed optimization requires nodes to coordinate, yet full synchronization scales poorly. When $n$ nodes collaborate through $m$ pairwise regularizers, standard methods demand $\mathcal{O}(m)$ communications per iteration. This paper proposes randomized local coordination: each node independently samples one regularizer uniformly and coordinates only with nodes sharing that term. This exploits partial separability, where each regularizer $G_j$ depends on a subset $S_j \subseteq \{1,\ldots,n\}$ of nodes. For graph-guided regularizers where $|S_j|=2$, expected communication drops to exactly 2 messages per iteration. This method achieves $\tilde{\mathcal{O}}(\varepsilon^{-2})$ iterations for convex objectives and under strong convexity, $\mathcal{O}(\varepsilon^{-1})$ to an $\varepsilon$-solution and $\mathcal{O}(\log(1/\varepsilon))$ to a neighborhood. Replacing the proximal map of the sum $\sum_j G_j$ with the proximal map of a single randomly selected regularizer $G_j$ preserves convergence while eliminating global coordination. Experiments validate both convergence rates and communication efficiency across synthetic and real-world datasets. |
| title | Decentralized Optimization with Topology-Independent Communication |
| topic | Machine Learning Optimization and Control 90C25, 68T05 G.1.6; C.2.4; I.2.6; F.2.1 |
| url | https://arxiv.org/abs/2509.14488 |