Backtracking line search

Imagine you want to climb a mountain, but you don't know the exact path to follow. You take a step forward, but it's too far away, and you get tired. You take a step backward, but it's too close, and you don't make progress. That's when you need to use a backtracking line search.

Backtracking line search is like finding the Goldilocks zone when climbing a mountain. You take a step forward, but instead of going all-in, you take small steps, and when you feel like you are getting tired or going way too fast or too slow, you step back, but not all the way. You go back just enough to make a small adjustment, and then you take another small step forward. This way, you ensure that you are moving in the right direction and not getting exhausted.

To put this into context in the world of data science, backtracking line search is a type of optimization technique used to find the optimal solution to a problem by taking small steps towards the solution while constantly adjusting the step sizes.

Suppose we have a mathematical function that we want to optimize by finding its minimum value. We might use backtracking line search to adjust the step size and direction to find the optimal value. We start with a large step size and keep reducing it until we find the minimum value of the function.

In summary, backtracking line search is a way to optimize a mathematical function by taking small steps towards the optimal solution while frequently readjusting the step sizes. It works like finding the Goldilocks zone while climbing a mountain – taking small steps forwards and backwards until you find the right balance.