How Stochastic Gradient Descent works part1(Machine Learning)

Abstract: In the machine learning literature stochastic gradient descent has recently been widely discussed for its purported implicit regularization properties. Much of the theory, that attempts to clarify the role of noise in stochastic gradient algorithms, has widely approximated stochastic gradient descent by a stochastic differential equation with Gaussian noise. Abstract: Stochastic Gradient Descent (SGD) has been the method of choice for learning large-scale non-convex models. While a general analysis of when SGD works has been elusive, there has been a lot of recent progress in understanding the convergence of Gradient Flow (GF) on the population loss, partly due to the simplicity that a continuous-time analysis buys us. An overarching theme of our paper is providing general conditions under which SGD converges, assuming that GF on the population loss converges.