variants

 

Gradient Descent algorithm and its variants

  • Difficulty Level : Easy
  • Last Updated : 15 Feb, 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.

What is Gradient Descent?

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.

How does Gradient Descent Work?

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.

Variants of Gradient Descent

1) Batch Gradient Descent: 

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.

2) Stochastic Gradient Descent (SGD): 

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.

3) Mini-Batch Gradient Descent: 

Mini-batch gradient descent is a compromise between batch gradient descent and SGD. The gradient of the loss function is computed with respect to a small randomly selected subset of the training examples (called a mini-batch), and the weights are updated after each mini-batch. Mini-batch gradient descent provides a balance between the stability of batch gradient descent and the computational efficiency of SGD.

4) Momentum: 

Momentum is a variant of gradient descent that incorporates information from the previous weight updates to help the algorithm converge more quickly to the optimal solution. Momentum adds a term to the weight update that is proportional to the running average of the past gradients, allowing the algorithm to move more quickly in the direction of the optimal solution.

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