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## Universal Algorithmic Intelligence: A mathematical top->down approach

Author:Marcus Hutter (2000-2007) Comments:70 pages Subj-class:Artificial Intelligence; Learning; Computational Complexity ACM-class:

I.2; F.1.3; E.4 Reference:Artificial General Intelligence (2007) pages 227-290, Springer Report-no:IDSIA-01-03 and cs.AI/0701125 Paper:LaTeX - PostScript - PDF - Html/Gif Slides:PostScript - PDF

Keywords:Artificial intelligence; algorithmic probability; sequential decision theory; rational agents; value function; Solomonoff induction; Kolmogorov complexity; reinforcement learning; universal sequence prediction; strategic games; function minimization; supervised learning.

Abstract:Decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. Solomonoff's theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameterless theory of universal Artificial Intelligence. We give strong arguments that the resulting AIXI model is the most intelligent unbiased agent possible. We outline for a number of problem classes, including sequence prediction, strategic games, function minimization, reinforcement and supervised learning, how the AIXI model can formally solve them. The major drawback of the AIXI model is that it is uncomputable. To overcome this problem, we construct a modified algorithm AIXI^{tl}, which is still effectively more intelligent than any other time t and spacelbounded agent. The computation time of AIXI^{tl}is of the ordert·2^{l}. Other discussed topics are formal definitions of intelligence order relations, the horizon problem and relations of the AIXI theory to other AI approaches.

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@InCollection{Hutter:07aixigentle, author = "Marcus Hutter", title = "Universal Algorithmic Intelligence: A Mathematical Top$\rightarrow$Down Approach", _oldtitle = "A Gentle Introduction to The Universal Algorithmic Agent {AIXI}", booktitle = "Artificial General Intelligence", editor = "B. Goertzel and C. Pennachin", publisher = "Springer", address = "Berlin", series = "Cognitive Technologies", _number = "IDSIA-01-03", _month = _jan, year = "2007", pages = "227--290", isbn = "3-540-23733-X", url = "http://www.hutter1.net/ai/aixigentle.htm", http = "http://arxiv.org/abs/cs.AI/0701125", ftp = "http://www.idsia.ch/idsiareport/IDSIA-01-03.ps.gz", categories = "I.2. [Artificial Intelligence]", keywords = "Artificial intelligence; algorithmic probability; sequential decision theory; rational agents; value function; Solomonoff induction; Kolmogorov complexity; reinforcement learning; universal sequence prediction; strategic games; function minimization; supervised learning.", abstract = "Decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. Solomonoff's theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameter-free theory of universal Artificial Intelligence. We give strong arguments that the resulting AIXI model is the most intelligent unbiased agent possible. We outline for a number of problem classes, including sequence prediction, strategic games, function minimization, reinforcement and supervised learning, how the AIXI model can formally solve them. The major drawback of the AIXI model is that it is uncomputable. To overcome this problem, we construct a modified algorithm AIXI$tl$ that is still effectively more intelligent than any other time $t$ and length $l$ bounded agent. The computation time of AIXI$tl$ is of the order $t \cdot 2^l$. Other discussed topics are formal definitions of intelligence order relations, the horizon problem and relations of the AIXI theory to other AI approaches.", }

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