Modeling AdaGrad, RMSProp, and Adam with Integro-Differential Equations

Fuente: arXiv
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Main Author: Heredia, Carlos
Format: Preprint
Published: 2024
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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
id 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