Gradient descent optimization algorithms

Gradient descent optimization algorithms is a widely used optimization algorithms in machine learning to minimize the cost function of a model. The cost function measures the difference between the predicted output and the actual output. Also, the objective is to find the set of parameters that minimize the cost function.

Gradient descent works by computing the gradient of the cost function concerning each parameter in the model. The gradient is a vector that points in the direction of the steepest ascent of the cost function. The opposite direction of the gradient points in the direction of the steepest descent. Which is the direction that minimizes the cost function.
The gradient descent algorithm adjusts the parameters in the direction of the negative gradient, which is equivalent to subtracting a small multiple of the gradient from the current value of the parameter. The amount of change is controlled by the learning rate, which is a hyperparameter that determines how much to adjust the parameters at each iteration. A high learning rate can cause the algorithm to overshoot the minimum and diverge, while a low learning rate can cause the algorithm to converge too slowly.

There are three types of gradient descent optimization algorithms:

1. Batch Gradient Descent: Batch gradient descent updates the parameters after evaluating the entire training set. It is computationally expensive for large datasets but gives accurate results.
2. Stochastic Gradient Descent (SGD): Stochastic gradient descent updates the parameters for each training example in the dataset. It is computationally efficient for large datasets but may have more oscillations around the optimal point.
3. Mini-batch Gradient Descent: Mini-batch gradient descent updates the parameters for a small random subset of the training set.

In addition to the basic gradient descent algorithm, several variations incorporate additional techniques to improve convergence and speed up the optimization process.
One such variation is momentum optimization, which adds a fraction of the previous update vector to the current update vector. Another variation is AdaGrad, which adapts the learning rate for each parameter based on the historical gradient.
RMSProp is another variation that uses an adaptive learning rate that takes into account the recent history of the gradients. Adam is a more sophisticated algorithm that combines the benefits of momentum and RMSProp. It provides faster convergence and better performance.