define Gradient Descent ?

 Gradient descent is an optimization algorithm used in various fields, including machine learning and mathematical optimization, to minimize a function by iteratively adjusting its parameters. The goal of gradient descent is to find the values of the parameters that result in the lowest possible value of the function.

The key idea behind gradient descent is to update the parameters of a model or system in the direction that leads to a decrease in the function's value. This direction is determined by the negative gradient of the function at the current point. The gradient is a vector that points in the direction of the steepest increase of the function, and taking its negative gives the direction of steepest decrease.

Here's a simplified step-by-step explanation of how gradient descent works:

1. Initialize the parameters of the model or system with some initial values.

2. Compute the gradient of the function with respect to the parameters at the current parameter values.

3. Update the parameters by subtracting a scaled version of the gradient from the current parameter values. This scaling factor is called the learning rate, which determines the step size in each iteration.

4. Repeat steps 2 and 3 until convergence criteria are met (e.g., the change in the function's value or parameters becomes very small, or a predetermined number of iterations is reached).

There are variations of gradient descent, such as stochastic gradient descent (SGD), mini-batch gradient descent, and more, which use subsets of the data to compute gradients, making the process more efficient for large datasets.

Gradient descent is crucial in training machine learning models, where the goal is often to find the optimal values of the model's parameters that minimize a loss function. By iteratively adjusting the parameters based on the negative gradient of the loss function, gradient descent helps models learn from data and improve their performance over time.