Gradient descent technique

Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for finding a local minimum of a differentiable multivariate function.

The core idea behind gradient descent is to iteratively adjust the parameters of the function in the opposite direction of the gradient of the function with respect to the parameters. This gradient, a vector of partial derivatives, points in the direction of the steepest increase of the function. By moving against the gradient, we aim to reduce the value of the function step by step.

In practice, the algorithm starts with an initial set of parameters and updates them iteratively. There are several variants of gradient descent:

  • Batch Gradient Descent: Uses the entire dataset to compute the gradient at each step. While this can be slow and computationally expensive for large datasets, it provides a stable and accurate estimate of the gradient.
  • Stochastic Gradient Descent (SGD): Uses a single randomly chosen data point to compute the gradient at each step. This can make the optimization process faster and allows for online learning, but it introduces noise in the gradient estimates, which can lead to a more erratic convergence path.
  • Mini-batch Gradient Descent: A compromise between batch and stochastic gradient descent. It uses a small, random subset of the data (a mini-batch) to compute the gradient. This approach balances the efficiency of SGD with the stability of batch gradient descent.

Gradient descent is widely used in machine learning, particularly for training neural networks and other complex models. It forms the backbone of many optimization algorithms due to its simplicity and effectiveness. However, gradient descent can struggle with issues such as choosing an appropriate learning rate, getting stuck in local minima or saddle points, and dealing with poorly conditioned optimization landscapes.

Various techniques, such as momentum, adaptive learning rates (e.g., AdaGrad, RMSprop, Adam), and gradient clipping, have been developed to address these challenges and improve the performance of gradient descent algorithms.