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Computer Science > Machine Learning

arXiv:2411.09734 (cs)
[Submitted on 14 Nov 2024]

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

Authors: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 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.
Comments: 22 pages
Subjects: Machine Learning (cs.LG); Numerical Analysis (math.NA); Optimization and Control (math.OC)
Cite as: arXiv:2411.09734 [cs.LG]
  (or arXiv:2411.09734v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2411.09734

Submission history

From: Carlos Heredia Pimienta [view email]
[v1] Thu, 14 Nov 2024 19:00:01 UTC (1,376 KB)
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