Free Lunch for Optimisation under the Universal Distribution

TL;DR

This paper challenges the No Free Lunch theorems by proposing a universal prior that allows for optimization advantages, demonstrating that under this prior, some algorithms outperform others without favoring specific function classes.

Contribution

It introduces a universal prior for function optimization that enables a free lunch, contrasting with the uniform assumption of the No Free Lunch theorems.

Findings

Existence of a universal prior allowing optimization advantages

Upper and lower bounds on the size of the free lunch

Contradicts the uniform assumption in No Free Lunch theorems

Abstract

Function optimisation is a major challenge in computer science. The No Free Lunch theorems state that if all functions with the same histogram are assumed to be equally probable then no algorithm outperforms any other in expectation. We argue against the uniform assumption and suggest a universal prior exists for which there is a free lunch, but where no particular class of functions is favoured over another. We also prove upper and lower bounds on the size of the free lunch.