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 gradient descent Not enough?

It can be very slow for very large datasets because only one-time update for each epoch so large number of epochs is required to have a substantial number of updates. For large datasets, the vectorization of data doesn't fit into memory. For non-convex surfaces, it may only find the local minimums.

What is the drawback of gradient descent approach?

Disadvantages of gradient descent: Can be very, very slow. The direction is not well-scaled. Therefore the number of iterations largely depends on the scale of the problem.

Is gradient descent optimal?

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.

Is SGD a greedy algorithm?

Here's how SGD+momentum works:

In non-momentum SGD, the parameters are updated via greedy search in the direction of the gradient. However, in SGD+momentum, the momentum additive from the previous steps influences the descent down the slope.

How Gradient Descent Works. Simple Explanation

Is gradient descent a heuristic?

Gradient-based methods are not considered heuristics or metaheuristics.

Why is gradient descent stochastic?

Stochastic Gradient Descent is a probabilistic approximation of Gradient Descent. It is an approximation because, at each step, the algorithm calculates the gradient for one observation picked at random, instead of calculating the gradient for the entire dataset.

Is gradient descent guaranteed to 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∗).

Is gradient descent Newton's method?

Newton's method has stronger constraints in terms of the differentiability of the function than gradient descent. If the second derivative of the function is undefined in the function's root, then we can apply gradient descent on it but not Newton's method.

What is the goal of gradient descent?

Similar to finding the line of best fit in linear regression, the goal of gradient descent is to minimize the cost function, or the error between predicted and actual y. In order to do this, it requires two data points—a direction and a learning rate.

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.

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 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.

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.

Why is SGD used instead of batch 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.

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.

Why is Newton Raphson better than gradient descent?

After reviewing a set of lectures on convex optimization, Newton's method seems to be a far superior algorithm than gradient descent to find globally optimal solutions, because Newton's method can provide a guarantee for its solution, it's affine invariant, and most of all it converges in far fewer steps.

Is Newtons 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).

What is the difference between Newton's method and gradient descent?

Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into account curvature information and thereby often improves convergence.

Does gradient descent always converge to global 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.

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.

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.

What is difference between gradient descent and stochastic gradient descent?

The only difference comes while iterating. In Gradient Descent, we consider all the points in calculating loss and derivative, while in Stochastic gradient descent, we use single point in loss function and its derivative randomly.

Is stochastic gradient descent faster?

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.

Is stochastic gradient descent supervised or unsupervised?

Gradient descent can be used for a whole bunch of unsupervised learning tasks. In fact, neural networks, which use the Gradient Descent algorithm are used widely for unsupervised learning tasks, like representations of text or natural language in vector space (word2vec).