An Efficient Stochastic Algorithm for Decentralized Nonconvex-Strongly-Concave Minimax Optimization
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866914794794123264 |
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| author | Chen, Lesi Ye, Haishan Luo, Luo |
| author_facet | Chen, Lesi Ye, Haishan Luo, Luo |
| contents | This paper studies the stochastic nonconvex-strongly-concave minimax optimization over a multi-agent network. We propose an efficient algorithm, called Decentralized Recursive gradient descEnt Ascent Method (DREAM), which achieves the best-known theoretical guarantee for finding the $ε$-stationary points. Concretely, it requires $\mathcal{O}(\min (κ^3ε^{-3},κ^2 \sqrt{N} ε^{-2} ))$ stochastic first-order oracle (SFO) calls and $\tilde{\mathcal{O}}(κ^2 ε^{-2})$ communication rounds, where $κ$ is the condition number and $N$ is the total number of individual functions. Our numerical experiments also validate the superiority of DREAM over previous methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_02387 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An Efficient Stochastic Algorithm for Decentralized Nonconvex-Strongly-Concave Minimax Optimization Chen, Lesi Ye, Haishan Luo, Luo Machine Learning Optimization and Control This paper studies the stochastic nonconvex-strongly-concave minimax optimization over a multi-agent network. We propose an efficient algorithm, called Decentralized Recursive gradient descEnt Ascent Method (DREAM), which achieves the best-known theoretical guarantee for finding the $ε$-stationary points. Concretely, it requires $\mathcal{O}(\min (κ^3ε^{-3},κ^2 \sqrt{N} ε^{-2} ))$ stochastic first-order oracle (SFO) calls and $\tilde{\mathcal{O}}(κ^2 ε^{-2})$ communication rounds, where $κ$ is the condition number and $N$ is the total number of individual functions. Our numerical experiments also validate the superiority of DREAM over previous methods. |
| title | An Efficient Stochastic Algorithm for Decentralized Nonconvex-Strongly-Concave Minimax Optimization |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2212.02387 |