gradientdesentalgoritme

Gradient descent is a first-order iterative optimization algorithm used to find a local minimum of a differentiable function. It is one of the most fundamental and widely used optimization algorithms in machine learning and deep learning. The core idea is to repeatedly move in the direction opposite to the gradient of the function at the current point. The gradient of a function indicates the direction of steepest ascent. Therefore, moving in the opposite direction of the gradient ensures a descent towards a minimum.

The algorithm starts with an initial guess for the parameters of the function. In each iteration, it calculates the gradient of the cost function with respect to each parameter. This gradient tells us how much the cost function changes for a small change in each parameter. The parameters are then updated by subtracting a fraction of the gradient from their current values. This fraction is controlled by a hyperparameter called the learning rate, which determines the size of the steps taken. A smaller learning rate leads to slower convergence but may avoid overshooting the minimum. A larger learning rate can speed up convergence but risks oscillating around the minimum or diverging.

The process continues until a convergence criterion is met, such as when the change in parameters or the cost function between iterations becomes very small, or after a fixed number of iterations. While gradient descent guarantees convergence to a local minimum for convex functions, it may converge to a suboptimal local minimum for non-convex functions. Variations like stochastic gradient descent (SGD) and mini-batch gradient descent are often used to accelerate training and escape local minima by using subsets of the data to compute the gradient.