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arXiv · 2411.09734

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

Carlos Heredia
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Abstract

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.

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Carlos Heredia. 2024-11-14. Modeling AdaGrad, RMSProp, and Adam with Integro-Differential Equations. https://arxiv.org/abs/2411.09734

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