A Comparison of Continuous-Time Approximations to Stochastic Gradient Descent

Applying a stochastic gradient descent (SGD) method for minimizing an objective gives rise to a discrete-time process of estimated parameter values. In order to better understand the dynamics of the estimated values, many authors have considered continuous-time approximations of SGD. We refine existing results on the weak error of first-order ODE and SDE approximations to SGD for non-infinitesimal learning rates. In particular, we explicitly compute the linear term in the error expansion of gradient flow and two of its stochastic …

authors comparison continuous dynamics error gradient process refine stochastic values