# Gradient Descent

## Definition of Gradient Descent

Gradient descent is a popular optimization algorithm used in machine learning and data science. The goal of gradient descent is to find the minimum value of a function by systematically decreasing its value in each iteration. The algorithm takes as input an initial guess for the solution, and the derivative of the function at that point. It then calculates the gradient of the function at that point, and uses that information to calculate a new direction in which to move toward the minimum value.

## How is Gradient Descent used?

Gradient Descent is a machine learning algorithm used to accurately model complex, non-linear relationships in data. It works by finding the optimal parameters for a given function or model that will minimize the overall error. This process involves taking small steps in the direction of steepest descent until an optimal set of parameters is found.

The gradient descent algorithm begins with some initial parameters and takes successive steps in the direction of steepest descent, i.e., towards a local minimal error value. During each step, the algorithm simultaneously calculates the partial derivatives for each parameter with respect to the overall error. Using this calculated information, it then adjusts all the parameters a small amount proportional to their respective partial derivatives. The magnitude of this adjustment is called the “learning rate”. After each adjustment, the total error value is recalculated and compared to determine whether improvements have been made or not. If an improvement was made, then another step is taken in that same direction; if not, then a different direction is chosen and tried again until an optimal solution has been reached where no further improvements can be made.

Gradient Descent can be used for many different types of optimization problems such as training neural networks and fitting linear or polynomial regression models. In addition to minimizing errors, it can also help maximize likelihoods when searching for an optimal set of parameters for a given problem or task (e.g., predicting stock prices).