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), the noisy updates can act as a double-edged sword. On one hand, the noise provides a certain level of randomness that allows the algorithm to escape local minima, as it does not follow the gradient direction strictly. This feature can be beneficial in complex optimization landscapes where multiple local minima exist. The inherent noise in the updates can help the model to explore a wider solution space, potentially finding better global minima.

On the other hand, the noise can lead to instability during convergence. Since each update is based on a single data point rather than the full batch, the paths that the optimization walks can be quite erratic. This means that while SGD may escape local minima, it might struggle to settle down near the global minimum, causing fluctuations around it rather than convergence.

To summarize, while the noisiness of SGD can be a useful feature for escaping local minima, it also introduces challenges in achieving stable convergence. Therefore, finding the right balance between the exploration due to noise and the stability required to converge is crucial for effectively using SGD in practice.