Stabilized Proximal-Point Methods for Federated Optimization
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929573407490048 |
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| author | Jiang, Xiaowen Rodomanov, Anton Stich, Sebastian U. |
| author_facet | Jiang, Xiaowen Rodomanov, Anton Stich, Sebastian U. |
| contents | In developing efficient optimization algorithms, it is crucial to account for communication constraints -- a significant challenge in modern Federated Learning. The best-known communication complexity among non-accelerated algorithms is achieved by DANE, a distributed proximal-point algorithm that solves local subproblems at each iteration and that can exploit second-order similarity among individual functions. However, to achieve such communication efficiency, the algorithm requires solving local subproblems sufficiently accurately resulting in slightly sub-optimal local complexity. Inspired by the hybrid-projection proximal-point method, in this work, we propose a novel distributed algorithm S-DANE. Compared to DANE, this method uses an auxiliary sequence of prox-centers while maintaining the same deterministic communication complexity. Moreover, the accuracy condition for solving the subproblem is milder, leading to enhanced local computation efficiency. Furthermore, S-DANE supports partial client participation and arbitrary stochastic local solvers, making it attractive in practice. We further accelerate S-DANE and show that the resulting algorithm achieves the best-known communication complexity among all existing methods for distributed convex optimization while still enjoying good local computation efficiency as S-DANE. Finally, we propose adaptive variants of both methods using line search, obtaining the first provably efficient adaptive algorithms that could exploit local second-order similarity without the prior knowledge of any parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07084 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stabilized Proximal-Point Methods for Federated Optimization Jiang, Xiaowen Rodomanov, Anton Stich, Sebastian U. Machine Learning Optimization and Control In developing efficient optimization algorithms, it is crucial to account for communication constraints -- a significant challenge in modern Federated Learning. The best-known communication complexity among non-accelerated algorithms is achieved by DANE, a distributed proximal-point algorithm that solves local subproblems at each iteration and that can exploit second-order similarity among individual functions. However, to achieve such communication efficiency, the algorithm requires solving local subproblems sufficiently accurately resulting in slightly sub-optimal local complexity. Inspired by the hybrid-projection proximal-point method, in this work, we propose a novel distributed algorithm S-DANE. Compared to DANE, this method uses an auxiliary sequence of prox-centers while maintaining the same deterministic communication complexity. Moreover, the accuracy condition for solving the subproblem is milder, leading to enhanced local computation efficiency. Furthermore, S-DANE supports partial client participation and arbitrary stochastic local solvers, making it attractive in practice. We further accelerate S-DANE and show that the resulting algorithm achieves the best-known communication complexity among all existing methods for distributed convex optimization while still enjoying good local computation efficiency as S-DANE. Finally, we propose adaptive variants of both methods using line search, obtaining the first provably efficient adaptive algorithms that could exploit local second-order similarity without the prior knowledge of any parameters. |
| title | Stabilized Proximal-Point Methods for Federated Optimization |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2407.07084 |