No Free Lunch Theorem, Inductive Skepticism, and the Optimality of Meta-induction

Abstract

The no free lunch theorem is a radicalized version of Hume’s induction skepticism. It asserts that relative to a uniform probability distribution over all possible worlds, all computable prediction algorithms—whether ‘clever’ inductive or ‘stupid’ guessing methods (etc.)—have the same expected predictive success. This theorem seems to be in conflict with results about meta-induction. According to these results, certain meta-inductive prediction strategies may dominate other (non-meta-inductive) methods in their predictive success (in the long run). In this article this conflict is analyzed and dissolved, by means of probabilistic analysis and computer simulation.