Free Lunches For Function And Program Induction

In this paper we prove that for a variety of practical problems and representations, there is a free lunch for search algorithms that specialise in the task of finding functions or programs that solve problems, such as genetic programming. In other words, not all such algorithms are equally good under all possible performance measures. We focus in particular on the case where the objective is to discover functions that fit sets of data-points - a task that we will call symbolic regression. We show under what conditions there is a free lunch for symbolic regression, highlighting that these are extremely restrictive.