Gradienttilasku

Gradienttilasku, also known as gradient descent, is a fundamental optimization algorithm used in machine learning and other fields to find the minimum of a function. It works by iteratively moving in the direction of the steepest descent of the function. The "gradient" refers to the vector of partial derivatives of the function, which indicates the direction of the greatest rate of increase. To find the minimum, we move in the opposite direction of the gradient.

The process begins with an initial guess for the parameters of the function. In each step, the gradient of the function is calculated at the current parameter values. This gradient tells us how to adjust the parameters to decrease the function's value. The parameters are then updated by subtracting a fraction of the gradient, where this fraction is determined by a learning rate. The learning rate is a crucial hyperparameter that controls the step size. A large learning rate can cause the algorithm to overshoot the minimum, while a small learning rate can lead to slow convergence.

Gradienttilasku is widely used for training machine learning models, such as neural networks, where the goal is to minimize a loss function. Variations of gradienttilasku, like stochastic gradient descent (SGD) and mini-batch gradient descent, are employed to handle large datasets more efficiently. These variations use subsets of the data to estimate the gradient, reducing computational cost per iteration. The algorithm continues to iterate until a convergence criterion is met, such as when the change in the function value or parameters becomes sufficiently small.