The uncomputability of AIXI is a bigger problem than this post makes it out to be. This uncomputability inserts a contradiction into any proof that relies on AIXI—the same contradiction as in Goedel’s Theorem. You can get around this contradiction instead by using approximations of AIXI, but the resulting proofs will be specific to those approximations, and you would need to prove additional theorems to transfer results between the approximations.
That’s a good point, I should add a section addressing this. I don’t know what you mean that it’s the same contradiction as in Goedel’s theorem though—I suppose AIXI is usually proven uncomputable by a diagonalization argument which is also a proof technique used in Goedel’s incompleteness theorem? But I am not sure how far that analogy goes.
The uncomputability of AIXI is a bigger problem than this post makes it out to be. This uncomputability inserts a contradiction into any proof that relies on AIXI—the same contradiction as in Goedel’s Theorem. You can get around this contradiction instead by using approximations of AIXI, but the resulting proofs will be specific to those approximations, and you would need to prove additional theorems to transfer results between the approximations.
That’s a good point, I should add a section addressing this. I don’t know what you mean that it’s the same contradiction as in Goedel’s theorem though—I suppose AIXI is usually proven uncomputable by a diagonalization argument which is also a proof technique used in Goedel’s incompleteness theorem? But I am not sure how far that analogy goes.