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This paper establishes for the first time the predictive performance of speedpriors and their computational complexity. A speed prior is essentially aprobability distribution that puts low probability on strings that are notefficiently computable. We propose a variant to the original speed prior(Schmidhuber, 2002), and show that our prior can predict sequences drawn fromprobability measures that are estimable in polynomial time. Our speed prior iscomputable in doubly-exponential time, but not in polynomial time. On apolynomial time computable sequence our speed prior is computable inexponential time. We show better upper complexity bounds for Schmidhuber'sspeed prior under the same conditions, and that it predicts deterministicsequences that are computable in polynomial time; however, we also show that itis not computable in polynomial time, and the question of its predictiveproperties for stochastic sequences remains open.

Loss Bounds and Time Complexity for Speed Priors