Do gradient descent methods always converge to similar points?

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

Does gradient descent converge?

Intuitively, this means that gradient descent is guaranteed to converge and that it converges with rate O(1/k). value strictly decreases with each iteration of gradient descent until it reaches the optimal value f(x) = f(x∗).

Does gradient descent always converge to the optimum?

Hence, gradient descent would be guaranteed to converge to a local or global optimum.

Does gradient descent always converge to a local minimum?

Gradient Descent is an iterative process that finds the minima of a function. This is an optimisation algorithm that finds the parameters or coefficients of a function where the function has a minimum value. Although this function does not always guarantee to find a global minimum and can get stuck at a local minimum.

Why does gradient descent not converge?

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 Works. Simple Explanation

What are some of the problems of gradient descent?

The problem with gradient descent is that the weight update at a moment (t) is governed by the learning rate and gradient at that moment only. It doesn't take into account the past steps taken while traversing the cost space.

What is the drawback of gradient descent algorithm?

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.

Why does gradient descent always find the global minima?

Gradient descent finds a global minimum in training deep neural networks despite the objective function being non-convex. The current paper proves gradient descent achieves zero training loss in polynomial time for a deep over-parameterized neural network with residual connections (ResNet).

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.

When the gradient descent method is started from a point near the solution it will converge very quickly?

When Newton's method is started from a point near the solution, it will converge very quickly. True. Correct!

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.

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.

Do all gradient descent algorithms lead to the same model provided you let them run long enough?

Do all Gradient Descent algorithms lead to the same model provided you let them run long enough? No. The issue is that stochastic gradient descent and mini-batch gradient descent have randomness built into them. This means that they can find their way to nearby the global optimum, but they generally don't converge.

Is gradient descent deterministic?

GD is deterministic, and the same constant initial condition will always lead to the same iterates. No filtration is involved, and unlike SGD the iteration is not a stochastic process. In this sense, GD with large LR works in a statistical sense.

Does gradient descent always decrease loss?

The gradient always points in the direction of steepest increase in the loss function. The gradient descent algorithm takes a step in the direction of the negative gradient in order to reduce loss as quickly as possible.

What is the order of convergence in the steepest descent algorithm?

The steepest descent method converges to the solution of f(z₁, z₂) in just one iteration as (-1.3158, −1.6142). The minimum point in the original design space is found by defining the inverse transformation as x = QDz. This gives the minimum point in the original design space as (-1/3, − 3/2).

Can gradient descent escape saddle points and why?

Although gradient descent (GD) almost always escapes saddle points asymptotically [Lee et al., 2016], this paper shows that even with fairly natural random initialization schemes and non-pathological functions, GD can be significantly slowed down by saddle points, taking exponential time to escape.

What is the difference between gradient descent and steepest descent?

Summary. The gradient is the directional derivative of a function. The directional of steepest descent (or ascent) is the direction amongst all nearby directions that lowers or raises the value of f the most.

What is gradient descent rule?

Gradient descent is an optimization algorithm which is commonly-used to train machine learning models and neural networks. Training data helps these models learn over time, and the cost function within gradient descent specifically acts as a barometer, gauging its accuracy with each iteration of parameter updates.

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.

How can we avoid local minima in 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.

What is the greatest disadvantage of gradient descent method compared to other gradient based methods *?

Batch Gradient Descent

Some disadvantages are the stable error gradient can sometimes result in a state of convergence that isn't the best the model can achieve. It also requires the entire training dataset be in memory and available to the algorithm.

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 benefits and the limitations of using stochastic gradient descent?

How does gradient descent algorithm work?

Gradient Descent Algorithm iteratively calculates the next point using gradient at the current position, then scales it (by a learning rate) and subtracts obtained value from the current position (makes a step). It subtracts the value because we want to minimise the function (to maximise it would be adding).