Improved stochastic gradient descent algorithm with mean-gradient adaptive stepsize for solving large-scale optimization problems

Stochastic gradient descent (SGD) is one of the most common algorithms used in solving large unconstrained optimization problems. It utilizes the concept of classical gradient descent method with modification on the gradient selection. SGD uses random or batch data sets to compute gradient in solving optimization problems. It is an iterative algorithm with descent properties that reduces computational cost by using derivatives of random data points. This paper proposes a new SGD algorithm with modified stepsize that employs function scaling strategy. Particularly, the stepsize parameter is coupled with function scaling by storing the mean of gradients in the denominator. The performance of the method is evaluated based on the ability to reduce function value after each iteration, ability to attain the lowest function value when applied to solve the well-known zebra-strip problem. Our results indicate that the proposed method performed favourable to the existing method.

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