User:Yuxin Zhou/No free lunch theorem

This article is about mathematical folklore. For treatment of the mathematics, see No free lunch in search and optimization.

In mathematical folklore, the "no free lunch" (NFL) theorem (sometimes pluralized) of David Wolpert and William Macready appears in the 1997 "No Free Lunch Theorems for Optimization". There is no free lunch in the world means that there is no such thing as a free lunch in the world. The analogy is that you have to work hard to do anything, don't think about getting something for nothing. It means that there will be no results without labor, and it also reminds people not to be greedy for cheap, and to be vigilant. Wolpert had previously derived no free lunch theorems for machine learning (statistical inference).

In 2005, Wolpert and Macready themselves indicated that the first theorem in their paper "state[s] that any two optimization algorithms are equivalent when their performance is averaged across all possible problems".

The "no free lunch" (NFL) theorem is an easily stated and easily understood consequence of theorems Wolpert and Macready actually prove. It is weaker than the proven theorems, and thus does not encapsulate them. Various investigators have extended the work of Wolpert and Macready substantively. See No free lunch in search and optimization for treatment of the research area.

While some scholars argue that NFL conveys important insight, others argue that NFL is of little relevance to machine learning research.