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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 AIXItl, which is still effectively more intelligent than any other time t and space l bounded agent. The computation time of AIXItl is of the order t·2l. 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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BibTeX Entry

@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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