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

• URL: http://arxiv.org/abs/2411.09734v1
• Date: Thu, 14 Nov 2024 19:00:01 GMT
• Title: Modeling AdaGrad, RMSProp, and Adam with Integro-Differential Equations
• Authors: Carlos Heredia,
• Abstract summary: We propose a continuous-time formulation for the AdaGrad, RMSProp, and Adam optimization algorithms. We perform numerical simulations of these equations to demonstrate their validity as accurate approximations of the original algorithms.
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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 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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