Free Lunch for Optimisation under the Universal Distribution
Tom Everitt, Tor Lattimore, Marcus Hütter · 2016
Abstract—Function optimisation is a major challenge in com-puter 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. I.