In Stochastic Gradient Descent, each update is noisier than in batch gradient descent, which can be a , but can also help escape

In Stochastic Gradient Descent (SGD), each update is indeed noisier compared to batch gradient descent. This is because SGD updates the model parameters for each training example one by one, as opposed to batch gradient descent which computes the gradient of the cost function based on the entire training dataset.

This can be a disadvantage because the frequent updates with a high variance can cause the cost function to fluctuate heavily and the algorithm may never converge to the minimum.

However, this can also be an advantage as this randomness can help the algorithm jump out of local minima, therefore SGD can lead to better solutions than batch gradient descent in some cases.

In other words, the noise in the SGD update process can act as a kind of implicit regularization, helping the model avoid overfitting the training data.