Gradient Descent

Gradient descent is an iterative optimization algorithm used to minimize a loss function in machine learning and statistical modeling. The algorithm operates by updating model parameters in the direction of the negative gradient of the loss function with respect to the parameters. Mathematically, the update rule can be expressed as θ := θ - η ∇L(θ), where θ represents the model parameters, η is the learning rate, and ∇L(θ) is the gradient of the loss function L with respect to θ. The choice of learning rate is critical, as it determines the step size taken towards the minimum; too large a value may lead to divergence, while too small a value can result in slow convergence. Gradient descent can be implemented in various forms, including batch gradient descent, stochastic gradient descent, and mini-batch gradient descent, each with distinct trade-offs in terms of convergence speed and computational efficiency. This method is foundational in training machine learning models, particularly in deep learning architectures.