Is it possible that gradient descent fails to find the minimum of a function?

Gradient descent can't tell whether a minimum it has found is local or global. The step size α controls whether the algorithm converges to a minimum quickly or slowly, or whether it diverges. Many real world problems come down to minimizing a function.

Does gradient descent always converge to minimum?

Gradient Descent need not always converge at global minimum. It all depends on following conditions; The function must be convex function.

Can gradient descent fail?

If the execution is not done properly while using gradient descent, it may lead to problems like vanishing gradient or exploding gradient problems. These problems occur when the gradient is too small or too large. And because of this problem the algorithms do not converge.

How gradient descent finds a minimum of a function?

Gradient descent is an efficient optimization algorithm that attempts to find a local or global minimum of the cost function. A local minimum is a point where our function is lower than all neighboring points. It is not possible to decrease the value of the cost function by making infinitesimal steps.

What are the problems involved with gradient descent procedures?

Gradient Descent, Step-by-Step

What are the limitations of gradient descent?

How does gradient descent avoid local minima?

Momentum, simply put, adds a fraction of the past weight update to the current weight update. This helps prevent the model from getting stuck in local minima, as even if the current gradient is 0, the past one most likely was not, so it will as easily get stuck.

Can gradient descent get stuck in a local minimum when training a linear regression model?

Can Gradient Descent get stuck in a local minimum when training a Logistic Regression model? Gradient descent produces a convex shaped graph which only has one global optimum. Therefore, it cannot get stuck in a local minimum.

Does gradient descent find local minima?

For smooth functions, gradient descent finds local minima. If the function is complicated, there may be no way to tell whether the solution is also a global minimum.

What are the conditions in which gradient descent is applied?

Gradient descent is best used when the parameters cannot be calculated analytically (e.g. using linear algebra) and must be searched for by an optimization algorithm.

Why is gradient descent bad?

It does not arrive exactly at the minimum — with the gradient descent, you are guaranteed to never get to the exact minimum, be it local or global one. That's because you are only as precise as the gradient and learning rate alpha. This may be quite a problem if you want a really accurate solution.

Can gradient descent get stuck?

The path of stochastic gradient descent wanders over more places, and thus is more likely to "jump out" of a local minimum, and find a global minimum (Note*). However, stochastic gradient descent can still get stuck in local minimum.

How do you not get stuck in local minima?

Ans: We can try to prevent our loss function from getting stuck in a local minima by providing a momentum value. So, it provides a basic impulse to the loss function in a specific direction and helps the function avoid narrow or small local minima. Use stochastic gradient descent.

Is it possible that the cost function goes up with each iteration of gradient descent in a neural network?

In Neural Networks, Gradient Descent looks over the entire training set in order to calculate gradient. The cost function decreases over iterations. If cost function increases, it is usually because of errors or inappropriate learning rate.

How gradient descent method is used for minimizing the cost function in Linear Regression?

Gradient Descent is the process of minimizing a function by following the gradients of the cost function. This involves knowing the form of the cost as well as the derivative so that from a given point you know the gradient and can move in that direction, e.g. downhill towards the minimum value.

What is the main drawback when using the gradient descent algorithm in higher dimensions?

The main disadvantages: It won't converge. On each iteration, the learning step may go back and forth due to the noise. Therefore, it wanders around the minimum region but never converges.

What are the advantages and disadvantages of gradient descent?

Some advantages of batch gradient descent are its computational efficient, it produces a stable error gradient and a stable convergence. Some disadvantages are the stable error gradient can sometimes result in a state of convergence that isn't the best the model can achieve.

What are the limitations of steepest descent algorithm?

The main observation is that the steepest descent direction can be used with a different step size than the classical method that can substantially improve the convergence. One disadvantage however is the lack of monotone convergence.

How do you find the minimum value of a function using differentiation?

To find the minimum value, substitute x = 2 in f(x). Substitute x = -1 in f"(x). To find the maximum value, substitute x = -1 in f(x).

How do you know if a point is maximum or minimum?

Do gradient descent methods always converge to same point?

No, they always don't. That's because in some cases it reaches a local minima or a local optima point.

What are general limitations of backward propagation?

One of the major disadvantages of the backpropagation learning rule is its ability to get stuck in local minima. The error is a function of all the weights in a multidimensional space.

Why is gradient descent efficient?

Gradient descent is an efficient optimization algorithm that attempts to find a local or global minimum of a function. Gradient Descent runs iteratively to find the optimal values of the parameters corresponding to the minimum value of the given cost function, using calculus.