Problem-Parameter-Free Decentralized Bilevel Optimization
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arXiv
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| Format: | Preprint |
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2025
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| author | Zhai, Zhiwei Yan, Wenjing Zhang, Ying-Jun Angela |
| author_facet | Zhai, Zhiwei Yan, Wenjing Zhang, Ying-Jun Angela |
| contents | Decentralized bilevel optimization has garnered significant attention due to its critical role in solving large-scale machine learning problems. However, existing methods often rely on prior knowledge of problem parameters-such as smoothness, convexity, or communication network topologies-to determine appropriate stepsizes. In practice, these problem parameters are typically unavailable, leading to substantial manual effort for hyperparameter tuning. In this paper, we propose AdaSDBO, a fully problem-parameter-free algorithm for decentralized bilevel optimization with a single-loop structure. AdaSDBO leverages adaptive stepsizes based on cumulative gradient norms to update all variables simultaneously, dynamically adjusting its progress and eliminating the need for problem-specific hyperparameter tuning. Through rigorous theoretical analysis, we establish that AdaSDBO achieves a convergence rate of $\widetilde{\mathcal{O}}\left(\frac{1}{T}\right)$, matching the performance of well-tuned state-of-the-art methods up to polylogarithmic factors. Extensive numerical experiments demonstrate that AdaSDBO delivers competitive performance compared to existing decentralized bilevel optimization methods while exhibiting remarkable robustness across diverse stepsize configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Problem-Parameter-Free Decentralized Bilevel Optimization Zhai, Zhiwei Yan, Wenjing Zhang, Ying-Jun Angela Optimization and Control Machine Learning Decentralized bilevel optimization has garnered significant attention due to its critical role in solving large-scale machine learning problems. However, existing methods often rely on prior knowledge of problem parameters-such as smoothness, convexity, or communication network topologies-to determine appropriate stepsizes. In practice, these problem parameters are typically unavailable, leading to substantial manual effort for hyperparameter tuning. In this paper, we propose AdaSDBO, a fully problem-parameter-free algorithm for decentralized bilevel optimization with a single-loop structure. AdaSDBO leverages adaptive stepsizes based on cumulative gradient norms to update all variables simultaneously, dynamically adjusting its progress and eliminating the need for problem-specific hyperparameter tuning. Through rigorous theoretical analysis, we establish that AdaSDBO achieves a convergence rate of $\widetilde{\mathcal{O}}\left(\frac{1}{T}\right)$, matching the performance of well-tuned state-of-the-art methods up to polylogarithmic factors. Extensive numerical experiments demonstrate that AdaSDBO delivers competitive performance compared to existing decentralized bilevel optimization methods while exhibiting remarkable robustness across diverse stepsize configurations. |
| title | Problem-Parameter-Free Decentralized Bilevel Optimization |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2510.24288 |