Gradienttilaskenta

Gradienttilaskenta, often referred to as gradient descent, is a fundamental optimization algorithm used in machine learning and various mathematical fields. Its primary purpose is to find the minimum of a function. The core idea is to iteratively adjust the parameters of a model in the direction opposite to the gradient of the cost function. The gradient, a vector of partial derivatives, indicates the direction of steepest ascent for the function at a given point. By moving in the negative gradient direction, the algorithm seeks to decrease the function's value, effectively moving towards a minimum.

The process begins with an initial set of parameter values. At each step, the gradient of the cost function with respect to these parameters is calculated. This gradient is then scaled by a learning rate, a small positive value that controls the size of the steps taken. The parameters are updated by subtracting the scaled gradient from their current values. This process is repeated until a convergence criterion is met, such as when the change in the cost function or parameters becomes sufficiently small, or after a predetermined number of iterations. Variations of gradient descent, such as stochastic gradient descent and mini-batch gradient descent, exist to improve efficiency and handle large datasets.