Neograd: Near-Ideal Gradient Descent

The purpose of this paper is to improve upon existing variants of gradient descent by solving two problems: (1) removing (or reducing) the plateau that occurs while minimizing the cost function,(2) continually adjusting the learning rate to an "ideal" value. The approach taken is to approximately solve for the learning rate as a function of a trust metric. When this technique is hybridized with momentum, it creates an especially effective gradient descent variant, called NeogradM. It is shown to outperform Adam on several test problems, and can easily reach cost function values that are smaller by a factor of $10^8$.