because often it isn’t known how to calculate it exactly

]]>but why would one use an approximation, when it is known how to calculate exactly ?

]]>http://en.wikipedia.org/wiki/Hoeffding%27s_inequality

http://en.wikipedia.org/wiki/Bernstein_inequalities_in_probability_theory

http://en.wikipedia.org/wiki/McDiarmid%27s_inequality#McDiarmid.27s_inequality

and many variants (data based, self-normalized, e.g., the book http://www.amazon.com/Self-Normalized-Processes-Statistical-Applications-Probability/dp/3540856358 etc.)

Ken,

See my comments below: What you may think is large, may not be so large. But I am not sure that machine learning people are indeed that worried. It just seems a cultural difference. Oh, and the bounds derived by machine learning people have often a different purpose: To characterize minimax rates for some class of problem or some procedure.