Common
No free lunch theorem
Mathematical folklore
No free lunch theorem
In mathematical folklore, the "no free lunch" (NFL) theorem (sometimes pluralized) of David Wolpert and William Macready, alludes to the saying "no such thing as a free lunch". In this case the intended meaning is that on the average there are no easy shortcuts to designing optimization algorithms. It appeared in the 1997 paper "No Free Lunch Theorems for Optimization". Wolpert had previously derived no free lunch theorems for machine learning. In 2005, Wolpert and Macready stated that the first theorem in their paper means 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 objectively weaker than the proven theorems, and thus does not encapsulate them. Various investigators have extended the work of Wolpert and Macready substantively. In terms of how the NFL theorem is used in...
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