Can gradient descent converge to zero?

We see above that gradient descent can reduce the cost function, and can converge when it reaches a point where the gradient of the cost function is zero.

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 happens when the gradient descent is zero?

Simple answer: it won't. Gradient descent climbs down a hill. If it reaches a plateau, it considers the algorithm converged and moves no more.

What does gradient descent converge to?

Setting ∇f(w)=0 gives a system of transcendental equations. But this objective function is convex and differentiable. So gradient descent converges to a global optimum.

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.

On the Global Convergence of Gradient Descent for (...) - Bach - Workshop 3 - CEB T1 2019

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.

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.

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.

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 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.

What's the assumption of gradient descent?

Stochastic gradient descent is based on the assumption that the errors at each point in the parameter space are additive. The error at point one can be added to the error at point two which can be added to the error at point three, and so on for all of the points.

What is the complexity of gradient descent?

Gradient descent has a time complexity of O(ndk), where d is the number of features, and n Is the number of rows. So, when d and n and large, it is better to use gradient descent.

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 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).

Is gradient descent deterministic?

Stochasticity of Deterministic Gradient Descent: Large Learning Rate for Multiscale Objective Function. This article suggests that deterministic Gradient Descent, which does not use any stochastic gradient approximation, can still exhibit stochastic behaviors.

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 happens if all the weights in the neural network are initialized to zero?

Zero initialization:

If all the weights are initialized to zeros, the derivatives will remain same for every w in W[l]. As a result, neurons will learn same features in each iterations. This problem is known as network failing to break symmetry. And not only zero, any constant initialization will produce a poor result.

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.

Is gradient descent a heuristic?

Gradient-based methods are not considered heuristics or metaheuristics.

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.

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.

Can stochastic gradient descent find global minimum?

The lowest point in the entire graph is the global minimum, which is what stochastic gradient descent attempts to find. Stochastic gradient descent attempts to find the global minimum by adjusting the configuration of the network after each training point.

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 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.

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.