Mini-batch descent in semiflows
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914163639451648 |
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| author | Corella, Alberto Domínguez Hernández, Martín |
| author_facet | Corella, Alberto Domínguez Hernández, Martín |
| contents | This paper investigates the application of mini-batch gradient descent to semiflows (gradient flows). Given a loss function (potential), we introduce a continuous version of mini-batch gradient descent by randomly selecting sub-loss functions over time, defining a piecewise flow. We prove that, under suitable assumptions on the potential generating the semiflow, the \textit{mini-batch descent flow} trajectory closely approximates the original semiflow trajectory on average. In addition, we study a randomized minimizing movement scheme that also approximates the semiflow of the full loss function. We illustrate the versatility of this approach across various problems, including constrained optimization, sparse inversion, and domain decomposition. Finally, we validate our results with several numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07556 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mini-batch descent in semiflows Corella, Alberto Domínguez Hernández, Martín Optimization and Control Numerical Analysis 34G25, 49J52, 37C10, 35K55, 37L05 This paper investigates the application of mini-batch gradient descent to semiflows (gradient flows). Given a loss function (potential), we introduce a continuous version of mini-batch gradient descent by randomly selecting sub-loss functions over time, defining a piecewise flow. We prove that, under suitable assumptions on the potential generating the semiflow, the \textit{mini-batch descent flow} trajectory closely approximates the original semiflow trajectory on average. In addition, we study a randomized minimizing movement scheme that also approximates the semiflow of the full loss function. We illustrate the versatility of this approach across various problems, including constrained optimization, sparse inversion, and domain decomposition. Finally, we validate our results with several numerical examples. |
| title | Mini-batch descent in semiflows |
| topic | Optimization and Control Numerical Analysis 34G25, 49J52, 37C10, 35K55, 37L05 |
| url | https://arxiv.org/abs/2407.07556 |