Solomonoff induction does have a blind spot: it assigns probability zero to the existence of halting oracles or other uncomputable sequences. Of course, every other computable prediction algorithm is just as incapable of predicting the output of a halting oracle and there don’t seem to be any uncomputable functions in the actual laws of physics, but it’s still a blind spot!
Is this something that the infra-bayesianism idea could address? So, would an infra-bayesian version of AIXI be able to handle worlds that include halting oracles, even though they aren’t exactly in its hypothesis class?
Solomonoff induction does have a blind spot: it assigns probability zero to the existence of halting oracles or other uncomputable sequences. Of course, every other computable prediction algorithm is just as incapable of predicting the output of a halting oracle and there don’t seem to be any uncomputable functions in the actual laws of physics, but it’s still a blind spot!
Is this something that the infra-bayesianism idea could address? So, would an infra-bayesian version of AIXI be able to handle worlds that include halting oracles, even though they aren’t exactly in its hypothesis class?