An Optimistic Gradient Tracking Method for Distributed Minimax Optimization
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908509605462016 |
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| author | Huang, Yan Xu, Jinming Chen, Jiming Johansson, Karl Henrik |
| author_facet | Huang, Yan Xu, Jinming Chen, Jiming Johansson, Karl Henrik |
| contents | This paper studies the distributed minimax optimization problem over networks. To enhance convergence performance, we propose a distributed optimistic gradient tracking method, termed DOGT, which solves a surrogate function that captures the similarity between local objective functions to approximate a centralized optimistic approach locally. Leveraging a Lyapunov-based analysis, we prove that DOGT achieves linear convergence to the optimal solution for strongly convex-strongly concave objective functions while remaining robust to the heterogeneity among them. Moreover, by integrating an accelerated consensus protocol, the accelerated DOGT (ADOGT) algorithm achieves an optimal convergence rate of $\mathcal{O} \left( κ\log \left( ε^{-1} \right) \right)$ and communication complexity of $\mathcal{O} \left( κ\log \left( ε^{-1} \right) /\sqrt{1-\sqrt{ρ_W}} \right)$ for a suboptimality level of $ε>0$, where $κ$ is the condition number of the objective function and $ρ_W$ is the spectrum gap of the network. Numerical experiments illustrate the effectiveness of the proposed algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Optimistic Gradient Tracking Method for Distributed Minimax Optimization Huang, Yan Xu, Jinming Chen, Jiming Johansson, Karl Henrik Optimization and Control Distributed, Parallel, and Cluster Computing This paper studies the distributed minimax optimization problem over networks. To enhance convergence performance, we propose a distributed optimistic gradient tracking method, termed DOGT, which solves a surrogate function that captures the similarity between local objective functions to approximate a centralized optimistic approach locally. Leveraging a Lyapunov-based analysis, we prove that DOGT achieves linear convergence to the optimal solution for strongly convex-strongly concave objective functions while remaining robust to the heterogeneity among them. Moreover, by integrating an accelerated consensus protocol, the accelerated DOGT (ADOGT) algorithm achieves an optimal convergence rate of $\mathcal{O} \left( κ\log \left( ε^{-1} \right) \right)$ and communication complexity of $\mathcal{O} \left( κ\log \left( ε^{-1} \right) /\sqrt{1-\sqrt{ρ_W}} \right)$ for a suboptimality level of $ε>0$, where $κ$ is the condition number of the objective function and $ρ_W$ is the spectrum gap of the network. Numerical experiments illustrate the effectiveness of the proposed algorithms. |
| title | An Optimistic Gradient Tracking Method for Distributed Minimax Optimization |
| topic | Optimization and Control Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2508.21431 |