2001/06/15 by Marcus Hutter · 1 citation
Computer Science · Mathematics · #cs.LG #cs.AI #cs.CC #math.PR
published as Lecture Notes in Artificial Intelligence (LNAI 2167), Proc. 12th Eurpean Conf. on Machine Learning (ECML) (2001) 239-250 · 11 LaTeX pages
arxiv created 2001/06/15 · arxiv updated 2009/11/30
Solomonoff's uncomputable universal prediction scheme ξ allows to predict the next symbol xk of a sequence x1...xk-1 for any Turing computable, but otherwise unknown, probabilistic environment μ. This scheme will be generalized to arbitrary environmental classes, which, among others, allows the construction of computable universal prediction schemes ξ. Convergence of ξ to μ in a conditional mean squared sense and with μ probability 1 is proven. It is shown that the average number of prediction errors made by the universal ξ scheme rapidly converges to those made by the best possible informed μ scheme. The schemes, theorems and proofs are given for general finite alphabet, which results in additional complications as compared to the binary case. Several extensions of the presented theory and results are outlined. They include general loss functions and bounds, games of chance, infinite alphabet, partial and delayed prediction, classification, and more active systems.