Continuous lunches are free
Olivier Teytaud and Anne Auger
In: GECCO 2007, 2007, London.
This paper investigates extensions of No Free Lunch (NFL)
theorems to countably inﬁnite and uncountable inﬁnite do-
mains. The original NFL due to Wolpert and Macready
states that all search heuristics have the same performance
when averaged over the uniform distribution over all possible
functions. For inﬁnite domains the extension of the concept
of distribution over all possible functions involves measur-
ability issues and stochastic process theory. For countably
inﬁnite domains, we prove that the natural extension of NFL
theorems does not hold, but that a weaker form of NFL does
hold, by stating the existence of non-trivial distributions of
ﬁtness leading to equal performance for all search heuristics.
Our main result is that for continuous domains, NFL does