Machine Dependence / Suboptimal Computation of the Data: Expected Loss Bounds

So far we have assumed the process computing the data is (asymptotically) optimally efficient, running on a particular universal computer, our reference machine. In general, however, we cannot know the machine used to run this process. Furthermore, the process may be nonoptimal even with respect to its machine. For such reasons we now relax our initial assumption, and show that -based predictions on our reference machine still work well.

Consider a finite but unknown program computing
.
What if Postulate 1 holds but is not optimally
efficient, and/or computed on a computer that differs from
our reference machine? Then we effectively do not sample
beginnings from but from an alternative semimeasure

for any whose computation through costs more than time. Can we still predict well? Yes, because the Speed Prior dominates : For all ,

(7) |

In practice we have to use
instead of .
Does that cost us a lot? Again
the answer is no, since for any ,

(8) |

(9) |

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