Gradient Descent is a first-order optimization algorithm that is widely used in machine learning and deep learning. It is used to find the minimum of a function by iteratively adjusting the parameters of a model.

Basic Concept

  • Objective Function: The function to be minimized, usually representing the error or loss in the model.
  • Parameters: The variables of the model that can be adjusted.
  • Gradient: The rate of change of the objective function with respect to each parameter.
  • Descent Step: The amount by which each parameter is adjusted to move towards the minimum.

Types of Gradient Descent

  1. Stochastic Gradient Descent (SGD): The gradient is computed using a single randomly selected training example at each iteration.
  2. Mini-batch Gradient Descent: The gradient is computed using a small batch of randomly selected training examples.
  3. Batch Gradient Descent: The gradient is computed using the entire training dataset.

Steps of Gradient Descent

  1. Initialize the parameters randomly.
  2. Compute the gradient of the objective function with respect to the parameters.
  3. Update the parameters using the gradient and a learning rate.
  4. Repeat steps 2 and 3 until convergence.

Learning Rate

The learning rate determines the size of the step taken in the direction of the gradient. A too large learning rate can cause divergence, while a too small learning rate can result in slow convergence.

Gradient Descent Visualization

For more information on Gradient Descent and its variations, check out our Introduction to Optimization Algorithms.