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.

Does SGD always decrease loss?

Why does SGD work? Unlike GD, SGD does not necessarily decrease the value of the loss at each step.

Does gradient descent always work?

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.

Does gradient descent always converge to the optimum What are the possibilities?

Gradient Descent is an algorithm which is designed to find the optimal points, but these optimal points are not necessarily global. And yes if it happens that it diverges from a local location it may converge to another optimal point but its probability is not too much.

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.

Gradient Descent, Step-by-Step

Is gradient descent a loss function?

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 are the limitations of gradient descent?

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.

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 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.

Is gradient descent optimal?

Gradient Descent is the most common optimization algorithm in machine learning and deep learning. It is a first-order optimization algorithm. This means it only takes into account the first derivative when performing the updates on the parameters.

How does gradient descent stop?

The actual stop point for gradient descent to stop running should be when step size approaches zero.

Why do we use gradient descent?

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.

What is an advantage of SGD over gradient descent?

It is easier to fit in the memory due to a single training example being processed by the network. It is computationally fast as only one sample is processed at a time. For larger datasets, it can converge faster as it causes updates to the parameters more frequently.

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.

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.

Does gradient descent give global minimum?

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).

Why is the gradient descent method chosen to minimize error?

This is because the result of a lower error between the actual and the predicted values means the algorithm has done a good job in learning. Gradient descent is an efficient optimization algorithm that attempts to find a local or global minimum of a function.

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.

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.

In which case the gradient descent algorithm works best?

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.

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.

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.

What is the advantage of stochastic gradient descent as compare to batch gradient descent?

SGD can be used when the dataset is large. Batch Gradient Descent converges directly to minima. SGD converges faster for larger datasets.

How do neural networks reduce loss?

Solutions to this are to decrease your network size, or to increase dropout. For example you could try dropout of 0.5 and so on. If your training/validation loss are about equal then your model is underfitting. Increase the size of your model (either number of layers or the raw number of neurons per layer)