New Stochastic Gradient Descent Algorithm via Lagrange-type 1-step-ahead Numerical Differentiation

The method that stochastic gradient descent (SGD) algorithm uses to update the undetermined parameter in the iterative process can be viewed as a rudimentary forward Euler method in the perspective of numerical differentiation. In order to overcome the connatural imperfection of the forward differentiation rule and computation error of the SGD algorithm, a new algorithm is obtained by substituting the original updating rule in SGD with the Lagrange-step l-step-ahead differentiation rule. In addition, extensive experiments between the original SGD algorithm and the modified algorithm are conducted to analyze the convergence. Empirical results demonstrate that Lagrange-step 1-step-ahead can not be used to the SGD algorithm and the new algorithm does not converge. Theoretical analysis is given to explain this result.