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passive_fist comments on Computation complexity of AGI design - Less Wrong
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Your premise is incorrect. AIXIt is not brute-force search of solutions. It is a true self-optimizing search; see arxiv.org/abs/cs/0004001. AIXI itself isn't a brute force search either. The basic AIXI model actually specifies no algorithmic implementation, so saying 'brute force search' is incorrect.
All your other arguments follow from this premise so they are also incorrect.
Solomonoff induction involves enumerating all possible program strings and testing for validity. There's another term for the class of algorithms which behave this way in the literature: it's called brute-force search.
(AIXI is not Solomonoff induction, it is reinforcement learning using Solomonoff induction to evaluate possible strategies. If I'm playing loose with terminology, it is here. But that technicality does not affect my argument.)
It's only brute-force search in the trivial sense that all search is brute-force search, at some level. See: No free lunch theorem.