What are the differences between gradient descent and the Newton method?

What are the differences between gradient descent and the Newton method?

Gradient descent is an iterative optimization algorithm that uses the gradient of the function to find the minimum, while the Newton method uses second-order derivatives (the Hessian) to find the minimum more quickly.

Which method is generally faster?

The Newton method can be faster because it uses curvature information, but it requires computing the Hessian, which can be expensive for large datasets.

Are there situations where gradient descent is preferred?

Yes, gradient descent is often preferred for large-scale problems or when the Hessian is difficult to compute, as it only requires first-order derivatives.

Can you give an example of when to use each method?

Use gradient descent for training deep learning models with large datasets, and the Newton method for smaller problems where precision is critical.

What are the limitations of each method?

Gradient descent can converge slowly and get stuck in local minima, while the Newton method can be computationally expensive and may not converge if the Hessian is not positive definite.