Continuous lunches are free!

Anne Auger (1) , Olivier Teytaud (1)

1 TANC - Algorithmic number theory for cryptology

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 distribution of fitness leading to equal performance for all search heuristics. Our main result is that for continuous domains, NFL does not hold.

Mots clés: Optimisation; Free lunches; NFL

Domaines: Optimisation et contrôle [math.OC]

Anne Auger, Olivier Teytaud. Continuous lunches are free!. GECCO, 2007, London, United Kingdom. ⟨inria-00173209⟩