Conclusion

Unlike the traditional universal prior , the Speed Prior 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 *non*computable 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 -based prediction is quite accurate as long as the true unknown prior is less dominant than , 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 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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