gradienttilaskentaa

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. Imagine a landscape with hills and valleys; gradient descent is like a person trying to find the lowest point in that landscape by always taking steps in the direction of the steepest downhill slope.

The core of gradient descent lies in calculating the gradient of the function. The gradient is a vector that points in the direction of the greatest rate of increase of a function at a given point. To find the minimum, we move in the opposite direction of the gradient, hence "descent". The size of each step is determined by a parameter called the learning rate. A larger learning rate means bigger steps, which can lead to faster convergence but risks overshooting the minimum. A smaller learning rate results in slower progress but a more precise approach to the minimum.

The algorithm is iterative. It starts with an initial guess for the parameters of the function. Then, it repeatedly calculates the gradient at the current position and updates the parameters by moving a small step in the negative gradient direction. This process continues until the algorithm converges, meaning the steps become very small, indicating that a minimum has been reached or is very close. Gradient descent is widely applied in training neural networks, where it's used to adjust the network's weights and biases to minimize the error or loss function.