The Speed Prior: A New Simplicity Measure Yielding Near-Optimal Computable Predictions
COLT '02 Proceedings of the 15th Annual Conference on Computational Learning Theory
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An algorithm M is described that solves any well-defined problem p as quickly as the fastest algorithm computing a solution to p, save for a factor of 5 and low-order additive terms. M optimally distributes resources between the execution of provably correct p-solving programs and an enumeration of all proofs, including relevant proofs of program correctness and of time bounds on program runtimes. M avoids Blum''s speed-up theorem by ignoring programs without correctness proof. M has broader applicability and can be faster than Levin''s universal search, the fastest method for inverting functions save for a large multiplicative constant. An extension of Kolmogorov complexity and two novel natural measures of function complexity are used to show that the most efficient program computing some function f is also among the shortest programs provably computing f.