I came across the formula for obtaining the upper confidence bounds on the k-armed bandit problem:
where $n_i$ is the amount of samples we have for this particular bandit and $N_i$ is the total amount of samples we have from all bandits. The same algorithm is used in the Monte Carlo Tree Search as well to obtain the upper confidence bound.
I understand very clearly what an upper confidence bound is, but what I don't understand is where this formula comes from. I have tried looking online in several places but could not find a clear explanation of how this formula is derived. Can someone please explain where this formula comes from? Please assume I don't have a great background in statistics.