AIXI-tl should handle your problem OK, since the relationship between hn and sn is irrelevant to the relationship between bn and rn. If it failed here it would fail for a problem with hn and sn random noise. However it might be possible to construct a more complex example where the fact that SHA512(sn)=hn is important for optimization of the reward...
I don’t think so. Imagine there were there were a way to determine weather a string is a valid hash, and it turned out that hn turned out not to be a valid hash. Then that information is relevant: you now know you are no longer playing the same game as the last times, and so you would no longer use the same strategy. From the perspective of AIXI-tl, not being able to prove that hn is a valid hash is treated the same as having a reliable indicator tell it that hn is not a valid hash, and it would act accordingly.
AIXI-tl should handle your problem OK, since the relationship between hn and sn is irrelevant to the relationship between bn and rn. If it failed here it would fail for a problem with hn and sn random noise. However it might be possible to construct a more complex example where the fact that SHA512(sn)=hn is important for optimization of the reward...
I don’t think so. Imagine there were there were a way to determine weather a string is a valid hash, and it turned out that hn turned out not to be a valid hash. Then that information is relevant: you now know you are no longer playing the same game as the last times, and so you would no longer use the same strategy. From the perspective of AIXI-tl, not being able to prove that hn is a valid hash is treated the same as having a reliable indicator tell it that hn is not a valid hash, and it would act accordingly.