What is asymptotic error? 
*

*Ng, A.Y., and Jordan, M.I. (2001). On Discriminative vs. Generative classifiers: A comparison of logistic regression and naive Bayes. Advances in Neural Information Processing Systems, 14, pp. 841-8, MIT Press.  


In the above paper, the authors mentioned "asymptotic error". Can anyone explain a bit about this?  
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"? 
 A: It means the error of a method when you run entire population through it. It's a useful measure of the method as it tells you what's the best you could get from a method. Also, you want to know how quickly the method converges to the asymptotic error, because you can't really run the population in most cases. 
A: 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.
A problem with this is that the terminal error may be only relatively constant, such that the language used is inexact. In the quote, "lower" means smaller absolute error, and "higher" means larger absolute error.
