Stochastic ADMM with batch size adaptation for nonconvex nonsmooth optimization
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911390794514432 |
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| author | Jin, Jiachen Deng, Kangkang Wang, Boyu Wang, Hongxia |
| author_facet | Jin, Jiachen Deng, Kangkang Wang, Boyu Wang, Hongxia |
| contents | Stochastic alternating direction method of multipliers (SADMM) is a popular method for solving nonconvex nonsmooth optimization in various applications. However, it typically requires an empirical selection of the static batch size for gradient estimation, resulting in a challenging trade-off between variance reduction and computational cost. This paper proposes adaptive batch size SADMM, a practical method that dynamically adjusts the batch size based on accumulated differences along the optimization path. We develop a simple convergence analysis to handle the dependence of batch size adaptation that matches the best-known complexity with flexible parameter choices. We further extend this adaptive scheme to reduce the overall complexity of the popular variance-reduced methods, SVRG-ADMM and SPIDER-ADMM. Numerical results validate the effectiveness of our proposed methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06921 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic ADMM with batch size adaptation for nonconvex nonsmooth optimization Jin, Jiachen Deng, Kangkang Wang, Boyu Wang, Hongxia Optimization and Control Stochastic alternating direction method of multipliers (SADMM) is a popular method for solving nonconvex nonsmooth optimization in various applications. However, it typically requires an empirical selection of the static batch size for gradient estimation, resulting in a challenging trade-off between variance reduction and computational cost. This paper proposes adaptive batch size SADMM, a practical method that dynamically adjusts the batch size based on accumulated differences along the optimization path. We develop a simple convergence analysis to handle the dependence of batch size adaptation that matches the best-known complexity with flexible parameter choices. We further extend this adaptive scheme to reduce the overall complexity of the popular variance-reduced methods, SVRG-ADMM and SPIDER-ADMM. Numerical results validate the effectiveness of our proposed methods. |
| title | Stochastic ADMM with batch size adaptation for nonconvex nonsmooth optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2505.06921 |