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G0W51 comments on Open Thread, May 25 - May 31, 2015 - Less Wrong Discussion
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Is Solomonoff induction a theorem for making optimal probability distributions or a definition of them? That is to say, has anyone proved that Solomonoff induction produces probability distributions that are "optimal," or was Solomonoff induction created to formalize what it means for a prediction to be optimal. In the former case, how could they define optimality?
Both, I think.
It surely is a nice formalization of Occam's razor, and Solomonoff himself said that he found his distribution while looking for a nice prior over the set of all computable hypothesis. But you can also show that Solomonoff distribution is in a class called dominant semi-measures, which are able to approximate any computable prior with an error that goes to zero very fast.
See for example "Solomonoff induction" by Legg.