Fehlergradienten

Fehlergradienten, also known as gradient descent, is a fundamental optimization algorithm used widely in machine learning and deep learning. Its primary purpose is to find the minimum of a function, typically a loss function, by iteratively moving in the direction of the steepest descent. The "gradient" refers to the vector of partial derivatives of the function with respect to its parameters. This gradient points in the direction of the greatest increase of the function. Therefore, by moving in the opposite direction of the gradient, we can effectively decrease the function's value.

The algorithm starts with an initial set of parameters. In each iteration, the gradient of the loss function is calculated at the current parameter values. This gradient is then used to update the parameters. The update rule is generally expressed as: new_parameters = current_parameters - learning_rate * gradient. The learning rate is a crucial hyperparameter that controls the step size of each update. A too-large learning rate can cause the algorithm to overshoot the minimum, while a too-small learning rate can lead to very slow convergence.

Fehlergradienten can be applied in various forms, such as batch gradient descent, where the gradient is computed using the entire training dataset, stochastic gradient descent (SGD), which uses a single training example per iteration, and mini-batch gradient descent, a compromise between the two that uses a small subset of the data. Each variant has its own trade-offs in terms of computational efficiency and convergence stability. Despite its simplicity, Fehlergradienten is a powerful tool for training complex models.