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arXiv · 1507.04121

Solomonoff Induction Violates Nicod's Criterion

Jan Leike·Marcus Hutter
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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.

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Jan Leike, Marcus Hutter. 2015-07-15. Solomonoff Induction Violates Nicod's Criterion. https://arxiv.org/abs/1507.04121

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