{"ID":2849045,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.24288","arxiv_id":"2510.24288","title":"Problem-Parameter-Free Decentralized Bilevel Optimization","abstract":"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.","short_abstract":"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 steps...","url_abs":"https://arxiv.org/abs/2510.24288","url_pdf":"https://arxiv.org/pdf/2510.24288v1","authors":"[\"Zhiwei Zhai\",\"Wenjing Yan\",\"Ying-Jun Angela Zhang\"]","published":"2025-10-28T10:50:04Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}