What is local minima in gradient descent?
Gradient descent techniques are known to be limited by a characteristic referred to as the `local minima’ problem. During the search for an optimum solution or global minima, these techniques can encounter local minima from which they cannot escape due to the `steepest descent’ nature of the approach.
How does stochastic gradient descent avoid local minima?
The stochastic gradient (SG) algorithm behaves like a simulated annealing (SA) algorithm, where the learning rate of the SG is related to the temperature of SA. The randomness or noise introduced by SG allows to escape from local minima to reach a better minimum.
Will Stochastic Gradient Descent always converge?
Gradient Descent need not always converge at global minimum. It all depends on following conditions; If the line segment between any two points on the graph of the function lies above or on the graph then it is convex function.
How does stochastic gradient descent avoid local minimums?
So, stochastic gradient descent is more able to avoid local minimum because the landscape of batch loss function is different than the loss function of whole dataset (the case when you calculate the losses on all data and then update parameters).
Is there a saddle point or a local minimum for gradient descent?
On the contrary, a local minimum means that the loss function increases in all directions at my current point. As you can imagine, this is unlikely in high-dimensional spaces. Regardless of whether you have a saddle point or a local minimum, the regular implementation of the gradient descent would encounter difficulties during training.
Why do we need different types of gradient descent?
In Short: We need these different ways of implementing gradient descent to address several issues we will most certainly encounter when training Neural Networks which are local minima and saddle points of the loss function and noisy gradients. More on that will be explained in the following article — nice 😉
What does a saddle point mean in stochastic descent?
The corresponding dimensional space where the loss function lives has the same number of dimensions as the number of weight parameters. A saddle point means that at my current point in the high dimensional space the loss goes down in one direction, while goes up in another direction.