I am reading a paper involving learning in Multi-armed bandit case (its okay if you don't know what that is. Just trying to give context here.) To give sample complexity lower bound, they reduce their problem to coin bias problem.
Coin bias problem: Suppose you have 2 random variables X1 and X2. $ Pr( X_1 = 1) = 1/2 + \epsilon$ and $ Pr( X_2 = 1) = 1/2 - \epsilon$. Goal is to find number of samples one would need before one can claim that the samples are from distribution 1 or 2 with sufficient confidence (probability at least $1 - \delta$).
Sample complexity lower bound: $ \Omega(\frac{\log(1/ \delta)}{\epsilon^2}) $
This is apparently a very old proof given by Chernoff in 1960s but I am not able to get my hands on the proof. I need to understand it because I am trying to do something similar and could use some ideas from the proof. The reference to this proof is a book "Neural Network Learning, Theoretical Foundations" to which I don't have access.
It would be very helpful if someone can help me at least with the idea of the proof.
PS: I confess this is not like the typical question one would post over here but I was just out of ideas. Please excuse me if this question feels out of place to you.