In order to incorporate information criteria, this study expands the mathematical formulation using an existing method from the literature. By striking a balance between prediction accuracy and model complexity, these criteria aim to tackle overfitting, a prevalent issue in supervised learning tasks. Many of the desirable features of unconstrained Newton techniques are also present in projected Newton methods for optimisation over convex sets. Numerical solutions to equations can be effectively achieved using the Newton-Raphson method, sometimes known as the Newton Method. Its foundation is the elementary principle of linear approximation, The goal of this research is to fill a need in the existing literature on machine learning and data mining by creating new supervised learning algorithms that can handle classification and regression problems.