Back

Gradient Descent

What is Gradient Descent? 

Gradient descent is an optimization algorithm used to minimize the loss function in machine learning and deep learning models. It works by iteratively adjusting the model's parameters in the direction of the steepest decrease in the loss function, which is typically represented by the gradient of the loss function with respect to the model's parameters. The goal of gradient descent is to find the optimal set of parameters that minimize the loss function, thereby improving the model's accuracy.

How Does Gradient Descent Work? 

Gradient descent involves the following steps:

  1. Initialize Parameters: The model's parameters (weights and biases) are initialized, usually with small random values.
  2. Compute Loss: The loss function, which measures the difference between the model's predictions and the actual target values, is calculated using the current parameters.
  3. Calculate Gradient: The gradient of the loss function with respect to each parameter is computed. The gradient is a vector that points in the direction of the steepest increase in the loss function.
  4. Update Parameters: The parameters are updated by moving them in the opposite direction of the gradient. The update rule is: θ=θ−η⋅∇J(θ)\theta = \theta - \eta \cdot \nabla J(\theta)θ=θ−η⋅∇J(θ) where θ\thetaθ represents the parameters, η\etaη is the learning rate, and ∇J(θ)\nabla J(\theta)∇J(θ) is the gradient of the loss function with respect to θ\thetaθ.
  5. Repeat: Steps 2-4 are repeated for a predefined number of iterations or until the loss function converges to a minimum.

Why is Gradient Descent Important?

  • Optimization: Gradient descent is the cornerstone of many optimization problems in machine learning, particularly for training models like linear regression, logistic regression, and neural networks.
  • Scalability: Gradient descent can be applied to large datasets and complex models, making it suitable for a wide range of applications.
  • Efficiency: When implemented with appropriate techniques like learning rate scheduling and momentum, gradient descent can efficiently converge to an optimal solution.

Conclusion 

Gradient descent is a fundamental optimization algorithm in machine learning that iteratively minimizes the loss function by updating the model's parameters in the direction of the steepest descent. Its simplicity, scalability, and effectiveness make it a widely used method for training various machine learning models.

‍