High Probability Guarantees for Random Reshuffling
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915939654565888 |
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| author | Yu, Hengxu Li, Xiao |
| author_facet | Yu, Hengxu Li, Xiao |
| contents | We consider the stochastic gradient method with random reshuffling ($\mathsf{RR}$) for tackling smooth nonconvex optimization problems. $\mathsf{RR}$ finds broad applications in practice, notably in training neural networks. In this work, we provide high probability complexity guarantees for this method. First, we establish a high probability ergodic sample complexity result (without taking expectation) for finding an $\varepsilon$-stationary point. Our derived complexity matches the best existing in-expectation one up to a logarithmic term while imposing no additional assumptions nor modifying $\mathsf{RR}$'s updating rule. Second, building on this analysis, we propose a simple stopping criterion embedded with a computable stopping test for $\mathsf{RR}$ (denoted as $\mathsf{RR}$-$\mathsf{sc}$). This criterion is guaranteed to be triggered after a finite number of iterations, enabling us to prove the same order high probability complexity for the returned last iterate. The fundamental ingredient in deriving the aforementioned results is a new concentration property for random reshuffling, which could be of independent interest. Finally, we conduct numerical experiments on small neural network training to support our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11841 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | High Probability Guarantees for Random Reshuffling Yu, Hengxu Li, Xiao Optimization and Control Machine Learning 90C30, 90C06, 90C26, 90C15 We consider the stochastic gradient method with random reshuffling ($\mathsf{RR}$) for tackling smooth nonconvex optimization problems. $\mathsf{RR}$ finds broad applications in practice, notably in training neural networks. In this work, we provide high probability complexity guarantees for this method. First, we establish a high probability ergodic sample complexity result (without taking expectation) for finding an $\varepsilon$-stationary point. Our derived complexity matches the best existing in-expectation one up to a logarithmic term while imposing no additional assumptions nor modifying $\mathsf{RR}$'s updating rule. Second, building on this analysis, we propose a simple stopping criterion embedded with a computable stopping test for $\mathsf{RR}$ (denoted as $\mathsf{RR}$-$\mathsf{sc}$). This criterion is guaranteed to be triggered after a finite number of iterations, enabling us to prove the same order high probability complexity for the returned last iterate. The fundamental ingredient in deriving the aforementioned results is a new concentration property for random reshuffling, which could be of independent interest. Finally, we conduct numerical experiments on small neural network training to support our theoretical findings. |
| title | High Probability Guarantees for Random Reshuffling |
| topic | Optimization and Control Machine Learning 90C30, 90C06, 90C26, 90C15 |
| url | https://arxiv.org/abs/2311.11841 |