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.

Can gradient descent fail?

A final limitation is that gradient descent only works when our function is differentiable everywhere. Otherwise we might come to a point where the gradient isn't defined, and then we can't use our update formula. Gradient descent fails for non-differentiable functions.

Which are the common problems with gradient descent?

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.

What is the drawback of gradient descent approach?

The disadvantage of Batch gradient descent –

1.It is less prone to local minima but in case it tends to local minima. It has no noisy step hence it will not be able to come out of it. 2. Although it is computationally efficient but not fast.

How can you avoid getting stuck in local minima gradient descent?

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.

How Gradient Descent Works. Simple Explanation

Can gradient descent stuck in local minima?

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.

Does gradient descent always converge?

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

What are the pros and cons 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 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 is the disadvantage batch gradient descent optimizer?

Disadvantages of Batch Gradient Descent

Sometimes a stable error gradient can lead to a local minima and unlike stochastic gradient descent no noisy steps are there to help get out of the local minima. The entire training set can be too large to process in the memory due to which additional memory might be needed.

How do you speed up gradient descent?

Gradient descent is an optimization algorithm that uses the gradient of the objective function to navigate the search space. Gradient descent can be accelerated by using momentum from past updates to the search position.

Why gradient descent isn't enough a comprehensive introduction to optimization algorithms in neural networks?

Why Gradient descent isn't enough: A comprehensive introduction to optimization algorithms in neural networks. The goal of neural networks is to minimize the loss, for producing better and accurate results. In order to minimize the loss, we need to update the internal learning parameters(especially weights and biases).

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.

What is better than gradient descent?

An interesting alternative to gradient descent is the population-based training algorithms such as the evolutionary algorithms (EA) and the particle swarm optimisation (PSO).

Why is gradient descent slow?

In short, the fact that the length of each step of gradient descent is proportional to the magnitude of the gradient means that often gradient descent starts off making significant progress but slows down significantly near minima and saddle points - a behavior we refer to as 'slow crawling'.

Is gradient descent greedy?

Gradient descent is an optimization technique that can find the minimum of an objective function. It is a greedy technique that finds the optimal solution by taking a step in the direction of the maximum rate of decrease of the function.

In which of the following curves gradient descent can get trapped in a saddle point?

For full batch gradient decent does it make sense that it can be trapped in saddle point, as the error function is constant.

Which gradient descent converges the fastest?

Mini Batch gradient descent: This is a type of gradient descent which works faster than both batch gradient descent and stochastic gradient descent.

Is gradient descent expensive?

(2) Each gradient descent step is too expensive. In regards to (1), comparing gradient descent with methods that take into account information about the second order derivatives, gradient descent tends to be highly inefficient in regards to improving the loss at each iteration.

Is stochastic gradient descent better than gradient descent?

SGD is stochastic in nature i.e it picks up a “random” instance of training data at each step and then computes the gradient making it much faster as there is much fewer data to manipulate at a single time, unlike Batch GD.

Why is stochastic gradient descent better?

SGD is much faster but the convergence path of SGD is noisier than that of original gradient descent. This is because in each step it is not calculating the actual gradient but an approximation. So we see a lot of fluctuations in the cost. But still, it is a much better choice.

How many iterations does gradient descent take?

t ≥ 2L[f(w0) − f∗] ϵ , so gradient descent requires t = O(1/ϵ) iterations to achieve ∇f(wk)2 ≤ ϵ. Gradient descent can be suitable for solving high-dimensional problems. Guaranteed progress bound if gradient is Lipschitz, based on norm of gradient. Practical step size strategies based on the progress bound.

How do you know when gradient descent converges?

In contrast, if we assume that f is strongly convex, we can show that gradient descent converges with rate O(ck) for 0 <c< 1. This means that a bound of f(x(k)) − f(x∗) ≤ ϵ can be achieved using only O(log(1/ϵ)) iterations. This rate is typically called “linear convergence.”

Is Newton's method faster than gradient descent?

The three plots show a comparison of Newton's Method and Gradient Descent. Gradient Descent always converges after over 100 iterations from all initial starting points. If it converges (Figure 1), Newton's Method is much faster (convergence after 8 iterations) but it can diverge (Figure 2).