Loss Bounds and Time Complexity for Speed Priors
This work addresses theoretical foundations for AI sequence prediction, but it is incremental as it builds on prior speed prior concepts.
The paper establishes predictive performance and computational complexity bounds for speed priors, showing that a proposed variant can predict sequences from polynomial-time estimable measures but is computable in doubly-exponential time, while Schmidhuber's prior predicts deterministic polynomial-time sequences but is not polynomial-time computable.
This paper establishes for the first time the predictive performance of speed priors and their computational complexity. A speed prior is essentially a probability distribution that puts low probability on strings that are not efficiently computable. We propose a variant to the original speed prior (Schmidhuber, 2002), and show that our prior can predict sequences drawn from probability measures that are estimable in polynomial time. Our speed prior is computable in doubly-exponential time, but not in polynomial time. On a polynomial time computable sequence our speed prior is computable in exponential time. We show better upper complexity bounds for Schmidhuber's speed prior under the same conditions, and that it predicts deterministic sequences that are computable in polynomial time; however, we also show that it is not computable in polynomial time, and the question of its predictive properties for stochastic sequences remains open.