Continuous Lunches Are Not Free

TL;DR

This paper clarifies a misconception about the No Free Lunch theorem in continuous domains, showing that NFL indeed applies universally, resolving previous contradictions in the literature.

Contribution

It provides a formal resolution to the apparent contradiction regarding NFL applicability in continuous domains, confirming its universal validity.

Findings

NFL holds for arbitrary domains and co-domains in continuous settings

Clarifies misconceptions from prior literature

Resolves apparent contradictions in theoretical assumptions

Abstract

Stemming from a paper of Auger and Teytaud, there is a common misconception that for continuous domains No Free Lunch (NFL) does not hold. However, Rowe, Vose, and Wright have demonstrated that NFL holds for arbitrary domains and co-domains. This paper resolves the apparent contradiction.