Stochastic Runge-Kutta methods and adaptive SGD-G2 stochastic gradient descent
Imen Ayadi, Gabriel Turinici · 2021
The minimization of the loss function is of paramount importance in deep neural networks. Many popular optimization algorithms have been shown to correspond to some evolution equation of gradient flow type. Inspired by the numerical schemes used for general evolution equations, we introduce a second-order stochastic Runge Kutta method and show that it yields a consistent procedure for the minimization of the loss function. In addition, it can be coupled, in an adaptive framework, with the Stochastic Gradient Descent (SGD) to adjust automatically the learning rate of the SGD. The resulting adaptive SGD, called SGD-G2, shows good results in terms of convergence speed when tested on standard data-sets.