Decentralized Optimization with Topology-Independent Communication

• URL: http://arxiv.org/abs/2509.14488v1
• Date: Wed, 17 Sep 2025 23:42:57 GMT
• Title: Decentralized Optimization with Topology-Independent Communication
• Authors: Ying Lin, Yao Kuang, Ahmet Alacaoglu, Michael P. Friedlander,
• Abstract summary: Distributed optimization requires nodes to coordinate, yet full synchronization scales poorly.<n>This paper proposes randomized local coordination: each node independently samples one regularizer uniformly and coordinates only with nodes sharing that term.<n>Experiments validate both convergence rates and communication efficiency across synthetic and real-world datasets.
• Score: 9.348335671378424
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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