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

Code

• github.com/carlosherediapimienta/numerical_simulations_nonlocal
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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.

Reproductions