Question

Why does the GD can converge to the local minimum even with fixed learning rate and we don't need to change it it in each step?

Answer 1

Gradient Descent can converge to a local minimum with a fixed learning rate because the gradients naturally diminish as the algorithm approaches the minimum, resulting in smaller parameter updates.

Step-by-step explanation:

Gradient Descent (GD) can converge to a local minimum with a fixed learning rate because as the algorithm progresses, the gradients tend to get smaller, making the updates to the parameters smaller as well. Even if the learning rate remains the same throughout the process, the diminishing gradients result in smaller changes, thereby allowing for the convergence towards a local minimum. Nonetheless, utilizing a fixed learning rate may mean the convergence process is less efficient compared to adaptive learning rate methods, which can accelerate training or assist in avoiding getting stuck in suboptimal local minima.