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Unlike the traditional universal prior $M$, the Speed Prior $S$ is recursively approximable with arbitrary precision. This allows for deriving an asymptotically optimal recursive way of computing predictions, based on a natural discount of the probability of data that is hard to compute by any method. This markedly contrasts with Solomonoff's traditional noncomputable approach to optimal prediction based on the weaker assumption of recursively computable priors that completely ignore resource limitations [24,25].

Our expected loss bounds building on Hutter's recent work show that $S$-based prediction is quite accurate as long as the true unknown prior is less dominant than $S$, reflecting an observation-generating process on some unknown computer that is not optimally efficient.

Assuming that our universe is sampled from a prior that does not dominate $S$ we obtain several nontrivial predictions for physics.

Acknowledgment. The material presented here is based on section 6 of [22]. Thanks to Ray Solomonoff, Leonid Levin, Marcus Hutter, Christof Schmidhuber, and an unknown reviewer, for useful comments.

Juergen Schmidhuber 2003-02-25

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