How gradient descent can converge to local minimum even learning rate is fixed?

How gradient descent can converge to local minimum even learning rate is fixed?

Types of Gradient Descent The learning rate is fixed. In theory, if the cost function has a convex function, it is guaranteed to reach the global minimum, else the local minimum in case the loss function is not convex. Batch Gradient descent uses a whole batch of the training set in every iteration of training.

How do I get out of local minima neural network?

How to get out of a local minimum ?

1. Use another activation function. Instead of using ReLu, you could try using Tanh.
2. Play with the learning rate of your optimizer.
3. Try using the BatchNormalization layer in Keras.

When does stochastic gradient descent converge to a global minimum?

Briefly, when the learning rates decrease with an appropriate rate, and subject to relatively mild assumptions, stochastic gradient descent converges almost surely to a global minimum when the objective function is convex or pseudoconvex, and otherwise converges almost surely to a local minimum.

How is stochastic gradient descent used in machine learning?

To economize on the computational cost at every iteration, stochastic gradient descent samples a subset of summand functions at every step. This is very effective in the case of large-scale machine learning problems. Fluctuations in the total objective function as gradient steps with respect to mini-batches are taken.

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.

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.