# What is asymptotic error?

For example, the abstract of the paper includes:

Discriminative learning has lower asymptotic error, a generative classifier may also approach its higher asymptotic error much faster.

What is the exact definition of "Asymptotic Error"?

What it means is just the error to which the algorithm is asymptotic. Suppose we have an error that is the limiting error that an algorithm can achieve after a number of iterations, no matter how many. The error for the $i^{th}$ iteration is then (typically) larger than the error associated with a limiting number of iterations. The text is comparing a larger terminal error that is quickly achieved for fewer iterations with a smaller terminal error that takes more iterations to achieve.