Clarification needed for Hoeffding Inequality

[aland]

It's remarkable to have the chance to ask the author a question about his book. Normally, and often, I go through life with questions like these unanswered. So I appreciate greatly a resource like this.

So, the LHS side of the Hoeffding inequality is a probability. And yet, the RHS, as best as I can tell, has a range from 0 to 2.

What am I missing?

[yaser]

Originally Posted by aland

It's remarkable to have the chance to ask the author a question about his book. Normally, and often, I go through life with questions like these unanswered. So I appreciate greatly a resource like this.

So, the LHS side of the Hoeffding inequality is a probability. And yet, the RHS, as best as I can tell, has a range from 0 to 2.

What am I missing?

You are correct. The RHS is an upper bound on the probability. Sometimes it's a meaningful bound and sometimes it's a trivial bound, but it is always a valid bound.