# Absolutely No Free Lunches!

arXiv: https://arxiv.org/abs/2005.04791 · HTML: https://mlsanity.com/paper/2005.04791/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2020.

## Built on by (most cited first, 4 of 4)

- [The no-free-lunch theorems of supervised learning](https://mlsanity.com/paper/2202.04513/) (2022)
- [A Topological Perspective on Causal Inference](https://mlsanity.com/paper/2107.08558/) (2021)
- [Solomonoff induction](https://mlsanity.com/paper/2603.20274/) (2026)
- [Understanding Generalization Requires Universal Induction](https://mlsanity.com/paper/2609.34458/) (2026)

## Abstract (arXiv)

This paper is concerned with learners who aim to learn patterns in infinite binary sequences: shown longer and longer initial segments of a binary sequence, they either attempt to predict whether the next bit will be a 0 or will be a 1 or they issue forecast probabilities for these events. Several variants of this problem are considered. In each case, a no-free-lunch result of the following form is established: the problem of learning is a formidably difficult one, in that no matter what method is pursued, failure is incomparably more common that success; and difficult choices must be faced in choosing a method of learning, since no approach dominates all others in its range of success. In the simplest case, the comparison of the set of situations in which a method fails and the set of situations in which it succeeds is a matter of cardinality (countable vs. uncountable); in other cases, it is a topological matter (meagre vs. co-meagre) or a hybrid computational-topological matter (effectively meagre vs. effectively co-meagre).