Question

Suppose you are running gradient descent. As we reach the local minima, the gradient descent needs to take smaller steps to avoid overshooting to the other side. Do we need to reduce the learning rate alpha to achieve that? If yes, please explain. If not, please clarify how we can achieve taking smaller steps.

1) Yes, we need to reduce the learning rate alpha to achieve smaller steps.
2) No, we do not need to reduce the learning rate alpha to achieve smaller steps.
3) Cannot be determined.
4) Not enough information provided.

Answer 1

Yes, the learning rate alpha needs to be reduced to achieve smaller steps to avoid overshooting the local minimum in gradient descent. This can be done dynamically with algorithms that adjust the learning rate based on past gradients.

Step-by-step explanation:

The answer to the student's question is 1) Yes, we need to reduce the learning rate alpha to achieve smaller steps.

As we approach a local minimum using gradient descent, it is important to adjust the size of our updates to avoid overshooting the minimum. One common method to achieve this is by reducing the learning rate, often denoted by alpha (α). The learning rate dictates the size of the steps taken towards the minimum. If the learning rate is too high, you may step over the minimum; if it's too low, the algorithm may take a very long time to converge, or get stuck in a sub-optimal minimum.

In practical implementations of gradient descent, such as adaptive learning rate algorithms, the learning rate can be adjusted dynamically. Algorithms like AdaGrad, RMSprop, and Adam adjust the learning rate during training for each parameter based on past gradients. This means that as gradient values get smaller as the function approaches a minimum, so do the steps, without manually changing the learning rate.