Why does gradient descent not converge?

Why does gradient descent not converge?

While it can be shown that the approximation error converges to zero if all four parameters are sent to infinity in the right order, we demonstrate in this paper that stochastic gradient descent fails to converge for ReLU networks if their depth is much larger than their width and the number of random initializations …

Under what conditions 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∗).

Do gradient descent methods always converge to the same point?

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

Does gradient descent always converge to a local minimum?

Gradient Descent is an iterative process that finds the minima of a function. Although this function does not always guarantee to find a global minimum and can get stuck at a local minimum. To understand the difference between local minima and global minima, take a look at the figure above.

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.

Does gradient descent get stuck in local minima?

However, stochastic gradient descent can still get stuck in local minimum. Note: It is common to keep the learning rate constant, in this case stochastic gradient descent does not converge; it just wanders around the same point.

Is it possible for gradient descent to converge?

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. The reason is that the step size might be too large that prompts it recede one optimal point and the probability that it oscillates is much more than convergence.

Is the probability of gradient descent always the same?

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.

Are there any non convergent algorithms in machine learning?

Asides from the points you mentioned (convergence to non-global minimums, and large step sizes possibly leading to non-convergent algorithms), “inflection ranges” might be a problem too. Consider the following “recliner chair” type of function.