Modeling AdaGrad, RMSProp, and Adam with Integro-Differential Equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911204703731712 |
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| author | Heredia, Carlos |
| author_facet | Heredia, Carlos |
| contents | In this paper, we propose a continuous-time formulation for the AdaGrad, RMSProp, and Adam optimization algorithms by modeling them as first-order integro-differential equations. We perform numerical simulations of these equations, along with stability and convergence analyses, to demonstrate their validity as accurate approximations of the original algorithms. Our results indicate a strong agreement between the behavior of the continuous-time models and the discrete implementations, thus providing a new perspective on the theoretical understanding of adaptive optimization methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_09734 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modeling AdaGrad, RMSProp, and Adam with Integro-Differential Equations Heredia, Carlos Machine Learning Numerical Analysis Optimization and Control In this paper, we propose a continuous-time formulation for the AdaGrad, RMSProp, and Adam optimization algorithms by modeling them as first-order integro-differential equations. We perform numerical simulations of these equations, along with stability and convergence analyses, to demonstrate their validity as accurate approximations of the original algorithms. Our results indicate a strong agreement between the behavior of the continuous-time models and the discrete implementations, thus providing a new perspective on the theoretical understanding of adaptive optimization methods. |
| title | Modeling AdaGrad, RMSProp, and Adam with Integro-Differential Equations |
| topic | Machine Learning Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2411.09734 |