A Two-timescale Primal-dual Algorithm for Decentralized Optimization with Compression
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909453537771520 |
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| author | Liu, Haoming Yau, Chung-Yiu Wai, Hoi-To |
| author_facet | Liu, Haoming Yau, Chung-Yiu Wai, Hoi-To |
| contents | This paper proposes a two-timescale compressed primal-dual (TiCoPD) algorithm for decentralized optimization with improved communication efficiency over prior works on primal-dual decentralized optimization. The algorithm is built upon the primal-dual optimization framework and utilizes a majorization-minimization procedure. The latter naturally suggests the agents to share a compressed difference term during the iteration. Furthermore, the TiCoPD algorithm incorporates a fast timescale mirror sequence for agent consensus on nonlinearly compressed terms, together with a slow timescale primal-dual recursion for optimizing the objective function. We show that the TiCoPD algorithm converges with a constant step size. It also finds an O(1 /T ) stationary solution after T iterations. Numerical experiments on decentralized training of a neural network validate the efficacy of TiCoPD algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05701 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Two-timescale Primal-dual Algorithm for Decentralized Optimization with Compression Liu, Haoming Yau, Chung-Yiu Wai, Hoi-To Optimization and Control This paper proposes a two-timescale compressed primal-dual (TiCoPD) algorithm for decentralized optimization with improved communication efficiency over prior works on primal-dual decentralized optimization. The algorithm is built upon the primal-dual optimization framework and utilizes a majorization-minimization procedure. The latter naturally suggests the agents to share a compressed difference term during the iteration. Furthermore, the TiCoPD algorithm incorporates a fast timescale mirror sequence for agent consensus on nonlinearly compressed terms, together with a slow timescale primal-dual recursion for optimizing the objective function. We show that the TiCoPD algorithm converges with a constant step size. It also finds an O(1 /T ) stationary solution after T iterations. Numerical experiments on decentralized training of a neural network validate the efficacy of TiCoPD algorithm. |
| title | A Two-timescale Primal-dual Algorithm for Decentralized Optimization with Compression |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2501.05701 |