---
date: '2024-12-14'
description: theorem stating that no optimization algorithm performs better than others across all possible problems, averaged over all cost functions.
id: No free lunch
modified: 2026-06-05 15:08:22 GMT-04:00
tags:
  - seed
title: No free lunch
created: '2024-12-14'
published: '2024-12-14'
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slug: thoughts/No-free-lunch
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---
The concept in computer science saying “no such thing as a free lunch”, or shortcut for success \[@Wolpert1997NoFreeLunch\]

> \[!theorem\] Theorem 1.
>
> For any algorithm $a_{1}$ and $a_{2}$ at iteration steps $m$:
>
> $$
> \sum_{f} P(d^y_m \mid f,m,a_{1}) = \sum_{f} P(d^y_m \mid f, m, a_2)
> $$
>
> where $d^y_m$ denotes the ordered set of size $m$ of the cost value $y$ associated to input values $x \in X$, $f: X \to Y$ is the function being optimized, and $P(d^y_m \mid f,m,a)$ is the conditional probability of obtaining given sequence of cost values from algorithm $a$ run $m$ times on function $f$