Principles of Solomonoff Induction and AIXI

  • Peter Sunehag
  • Marcus Hutter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7070)

Abstract

We identify principles characterizing Solomonoff Induction by demands on an agent’s external behaviour. Key concepts are rationality, computability, indifference and time consistency. Furthermore, we discuss extensions to the full AI case to derive AIXI.

Keywords

Computability Representation Rationality Solomonoff induction 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    de Finetti, B.: La prévision: Ses lois logiques, ses sources subjectives. In: Annales de l’Institut Henri Poincar, Paris, vol. 7, pp. 1–68 (1937)Google Scholar
  2. 2.
    Diestel, J.: Sequences and series in Banach spaces. Springer (1984)Google Scholar
  3. 3.
    Dowe, D.L.: MML, hybrid bayesian network graphical models, statistical consistency, invariance and uniqueness. In: Handbook of the Philosophy of Science, HPS. Philosophy of Statistics, vol. 7, pp. 901–982 (2011)Google Scholar
  4. 4.
    Grünwald, P.: The Minimum Description Length Principle. MIT Press Books, The MIT Press (2007)Google Scholar
  5. 5.
    Hutter, M.: Universal Artificial Intelligence: Sequential Decisions based on Algorithmic Probability. Springer, Berlin (2005)Google Scholar
  6. 6.
    Hutter, M.: On universal prediction and Bayesian confirmation. Theoretical Computer Science 384, 33–48 (2007)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Kreyszig, E.: Introductory Functional Analysis With Applications. Wiley (1989)Google Scholar
  8. 8.
    Li, M., Vitányi, P.: Kolmogorov Complexity and its Applications. Springer (2008)Google Scholar
  9. 9.
    Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press (1944)Google Scholar
  10. 10.
    Ramsey, F.: Truth and probability. In: Braithwaite, R.B. (ed.) The Foundations of Mathematics and other Logical Essays, ch. 7, pp. 156–198. Brace & Co. (1931)Google Scholar
  11. 11.
    Rathmanner, S., Hutter, M.: A philosophical treatise of universal induction. Entropy 13(6), 1076–1136 (2011)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Rissanen, J.: Modeling By Shortest Data Description. Automatica 14, 465–471 (1978)CrossRefMATHGoogle Scholar
  13. 13.
    Rissanen, J.: Minimum description length principle. In: Sammut, C., Webb, G. (eds.) Encyclopedia of Machine Learning, pp. 666–668. Springer (2010)Google Scholar
  14. 14.
    Savage, L.: The Foundations of Statistics. Wiley, New York (1954)MATHGoogle Scholar
  15. 15.
    Sutton, R., Barto, A.: Reinforcement Learning: An Introduction (Adaptive Computation and Machine Learning). The MIT Press (March 1998)Google Scholar
  16. 16.
    Sunehag, P., Hutter, M.: Axioms for rational reinforcement learning. In: Kivinen, J., Szepesvári, C., Ukkonen, E., Zeugmann, T. (eds.) ALT 2011. LNCS, vol. 6925, pp. 338–352. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  17. 17.
    Solomonoff, R.: A Preliminary Report on a General Theory of Inductive Inference. Report V-131, Zator Co., Cambridge, Ma. (1960)Google Scholar
  18. 18.
    Solomonoff, R.J.: Complexity-based induction systems: comparisons and convergence theorems. IEEE Transactions on Information Theory 24, 422–432 (1978)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Solomonoff, R.J.: Does algorithmic probability solve the problem of induction? In: Proceedings of the Information, Statistics and Induction in Science Conferece (1996)Google Scholar
  20. 20.
    Sugden, R.: Rational choice: A survey of contributions from economics and philosophy. Economic Journal 101(407), 751–785 (1991)CrossRefGoogle Scholar
  21. 21.
    Turing, A.M.: On Computable Numbers, with an application to the Entscheidungsproblem. Proc. London Math. Soc. 2(42), 230–265 (1936)MathSciNetGoogle Scholar
  22. 22.
    Wallace, C.S.: Statistical and Inductive Inference by Minimum Message Length. Information Science and Statistics. Springer (2005)Google Scholar
  23. 23.
    Wallace, C.S., Boulton, D.M.: An information measure for classification. Computer Journal 11, 185–194 (1968)CrossRefMATHGoogle Scholar
  24. 24.
    Wallace, C.S., Dowe, D.L.: Minimum message length and Kolmogorov complexity. Computer Journal 42, 270–283 (1999)CrossRefMATHGoogle Scholar
  25. 25.
    Wood, I., Sunehag, P., Hutter, M. (Non-) Equivalence of universal priors. In: Proc. of Solomonoff Memorial Conference, Melbourne, Australia (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Peter Sunehag
    • 1
  • Marcus Hutter
    • 1
    • 2
  1. 1.Research School of Computer ScienceAustralian National UniversityCanberraAustralia
  2. 2.Department of Computer ScienceETH ZurichSwitzerland

Personalised recommendations