Solomonoff Induction Violates Nicod's Criterion
Abstract
Nicod's criterion states that observing a black raven is evidence for the hypothesis H that all ravens are black. We show that Solomonoff induction does not satisfy Nicod's criterion: there are time steps in which observing black ravens decreases the belief in H. Moreover, while observing any computable infinite string compatible with H, the belief in H decreases infinitely often when using the unnormalized Solomonoff prior, but only finitely often when using the normalized Solomonoff prior. We argue that the fault is not with Solomonoff induction; instead we should reject Nicod's criterion.
Cite
Text
Leike and Hutter. "Solomonoff Induction Violates Nicod's Criterion." International Conference on Algorithmic Learning Theory, 2015. doi:10.1007/978-3-319-24486-0_23Markdown
[Leike and Hutter. "Solomonoff Induction Violates Nicod's Criterion." International Conference on Algorithmic Learning Theory, 2015.](https://mlanthology.org/alt/2015/leike2015alt-solomonoff/) doi:10.1007/978-3-319-24486-0_23BibTeX
@inproceedings{leike2015alt-solomonoff,
title = {{Solomonoff Induction Violates Nicod's Criterion}},
author = {Leike, Jan and Hutter, Marcus},
booktitle = {International Conference on Algorithmic Learning Theory},
year = {2015},
pages = {349-363},
doi = {10.1007/978-3-319-24486-0_23},
url = {https://mlanthology.org/alt/2015/leike2015alt-solomonoff/}
}