1, slow convergence. Gradient descent method is a first-order convergent optimization algorithm with slow descent speed.

2, depending on gradient information. Each iteration needs to recalculate the gradient, and the descent process is unstable. If the objective function is nondifferentiable, the algorithm will fail directly.

3, vulnerable to local extreme points. If the objective function is not a convex function, but a function with multiple minima, mathematically speaking, the gradients of local extremum and global extremum are all 0, so the gradient descent method is easily limited by local extremum.

Knowledge expansion

Gradient is a mathematical concept that describes the maximum value of the directional derivative of a vector (function) at a certain point. In calculus and vector analysis, gradient is a very important concept, which can represent the maximum value of directional derivative of a function at a certain point.

The calculation method of gradient is simple. Suppose there is a function f(x), and the gradient at point X is the maximum of all partial derivatives at that point. In other words, if the partial derivatives of f(x) exist at point X, then the gradient is the maximum of these partial derivatives.

Gradient is widely used. Gradient descent method is a common method in machine learning and optimization algorithm. This method can minimize the objective function by calculating the gradient of the objective function at a certain point and then updating the parameters in the negative gradient direction. Gradient descent method is very effective in dealing with large-scale data sets and complex models.

However, the gradient descent method also has some disadvantages. First, it is very sensitive to initial values. If the initial value is not selected properly, the algorithm may fall into local minima and cannot find the global minima. Secondly, the gradient descent method needs to calculate all the partial derivatives of the objective function, which may be very time-consuming when dealing with complex models.

In addition, the gradient descent method may fluctuate and stagnate in the optimization process, which requires some skills to control the learning rate and the step size of the optimization algorithm.

In addition, the calculation of gradient also needs to pay attention to some details. If the partial derivative of the function does not exist at a certain point, then the gradient cannot be calculated. In addition, in some cases, the calculation of gradient may involve the process of seeking limit and derivative, which requires certain mathematical skills and experience.

In a word, gradient is a very important mathematical concept, which is widely used in calculus, vector analysis and machine learning. Although the gradient descent method has some shortcomings and limitations, it is still a very effective optimization algorithm, which can deal with large-scale data sets and complex models.