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# Gradient Descent algorithm and its variants

• Difficulty Level : Easy
• Last Updated : 01 Mar, 2023

Gradient descent is a powerful optimization algorithm used to minimize the loss function in a machine learning model. It’s a popular choice for a variety of algorithms, including linear regression, logistic regression, and neural networks. In this article, we’ll cover what gradient descent is, how it works, and several variants of the algorithm that are designed to address different challenges and provide optimizations for different use cases.

Gradient Descent is an iterative optimization algorithm used to minimize the cost function of a machine learning model. The idea is to move in the direction of the steepest descent of the cost function to reach the global minimum or a local minimum. Here are the steps involved in the Gradient Descent algorithm:

Initialize the parameters of the model with random values.
Calculate the gradient of the cost function with respect to each parameter.
Update the parameters by subtracting a fraction of the gradient from each parameter. This fraction is called the learning rate, which determines the step size of the algorithm.
Repeat steps 2 and 3 until convergence, which is achieved when the cost function stops improving or reaches a predetermined threshold.
There are several variants of the Gradient Descent algorithm, which differ in the way they calculate the updates to the parameters:

Batch Gradient Descent: In this variant, the entire training dataset is used to calculate the gradient and update the parameters. This can be slow for large datasets, but it ensures convergence to the global minimum.

Stochastic Gradient Descent (SGD): In this variant, only one random training example is used to calculate the gradient and update the parameters. This can be faster than Batch Gradient Descent, but the updates can be noisy and may not converge to the global minimum.

Mini-Batch Gradient Descent: In this variant, a small subset of the training dataset is used to calculate the gradient and update the parameters. This is a compromise between Batch Gradient Descent and SGD, as it is faster than Batch Gradient Descent and less noisy than SGD.

Momentum-based Gradient Descent: In this variant, the updates to the parameters are based on the current gradient and the previous updates. This helps the algorithm to overcome local minima and accelerate convergence.

RMSprop: In this variant, the learning rate is adaptively scaled for each parameter based on the moving average of the squared gradient. This helps the algorithm to converge faster in the presence of noisy gradients.

Adam: In this variant, the learning rate is adaptively scaled for each parameter based on the moving average of the gradient and the squared gradient. This combines the benefits of Momentum-based Gradient Descent, Adagrad, and RMSprop, and is one of the most popular optimization algorithms for deep learning.

Gradient descent is an optimization algorithm that is used to minimize the loss function in a machine learning model. The goal of gradient descent is to find the set of weights (or coefficients) that minimize the loss function. The algorithm works by iteratively adjusting the weights in the direction of the steepest decrease in the loss function.

The basic idea of gradient descent is to start with an initial set of weights and update them in the direction of the negative gradient of the loss function. The gradient is a vector of partial derivatives that represents the rate of change of the loss function with respect to the weights. By updating the weights in the direction of the negative gradient, the algorithm moves towards a minimum of the loss function.

The learning rate is a hyperparameter that determines the size of the step taken in the weight update. A small learning rate results in a slow convergence, while a large learning rate can lead to overshooting the minimum and oscillating around the minimum. It’s important to choose an appropriate learning rate that balances the speed of convergence and the stability of the optimization.

In batch gradient descent, the gradient of the loss function is computed with respect to the weights for the entire training dataset, and the weights are updated after each iteration. This provides a more accurate estimate of the gradient, but it can be computationally expensive for large datasets.

In SGD, the gradient of the loss function is computed with respect to a single training example, and the weights are updated after each example. SGD has a lower computational cost per iteration compared to batch gradient descent, but it can be less stable and may not converge to the optimal solution.