Beyond No Free Lunch: Realistic Algorithms for Arbitrary Problem Classes

TL;DR

This paper refines the understanding of the No Free Lunch theorem by identifying conditions under which it applies and demonstrates that revisiting algorithms are generally outperformed by enumerative algorithms under a new performance framework.

Contribution

It introduces a simplified condition for NFL applicability and a refined performance measure showing the superiority of enumerative algorithms over revisiting ones.

Findings

NFL applies when objective functions are permutation-closed.

Revisiting algorithms are always outperformed by enumerative algorithms under the new performance measure.

Quantifies how non-permutation-closed objectives affect algorithm performance.

Abstract

We show how the necessary and sufficient conditions for the NFL to apply can be reduced to the single requirement of the set of objective functions under consideration being closed under permutation, and quantify the extent to which a set of objectives not closed under permutation can give rise to a performance difference between two algorithms. Then we provide a more refined definition of performance under which we show that revisiting algorithms are always trumped by enumerative ones.