Learning Artificial Intelligence - Part 11 (Gradient Descent)

Gradient Descent is an iterative optimization algorithm used to find the minimum of a function, typically in the context of machine learning and deep learning for training models. The objective is to update the parameters of a model in such a way that the value of the function is minimized.

In a simplified explanation, here's how the Gradient Descent algorithm works:

Define the Objective Function: 

First, you need to have a differentiable objective function that you want to minimize. In the context of machine learning, this function is usually the "loss function" that measures the error or discrepancy between the predicted outputs of the model and the actual targets.

Initialize Parameters: 

You start by initializing the parameters (weights and biases) of the model with some random values.

Compute the Gradient: 

The next step is to compute the gradient (a vector of partial derivatives) of the objective function with respect to each parameter. The gradient points in the direction of the steepest increase in the function. In order to minimize the function, we move in the opposite direction of the gradient.

Update Parameters: 

With the gradient information, you update the parameters of the model. The magnitude of the update is controlled by a learning rate hyper parameter, which determines the step size of each iteration. Smaller learning rates result in slower convergence, while larger ones may lead to overshooting the minimum.

Iterate: 

Repeat steps 3 and 4 for a fixed number of iterations or until a convergence criterion is met (e.g., the change in the objective function becomes smaller than a certain threshold).

The process continues iteratively, and the model's parameters are updated in the direction that reduces the value of the objective function (i.e., the loss). By repeating this process, the model gradually converges to a set of parameter values that ideally correspond to the minimum of the objective function, effectively optimizing the model for the task at hand.

There are different variants of Gradient Descent, such as Stochastic Gradient Descent (SGD), Mini-Batch Gradient Descent, and variants with adaptive learning rates like Adam (Adaptive Moment Estimation). These variations address issues such as computational efficiency and better convergence performance.

It's essential to tune hyper parameters like the learning rate and the batch size (in the case of mini-batch gradient descent) to ensure effective and stable training of machine learning models.