Stochastic Tasks: Difficulty and Levin Search

  • José Hernández-OralloEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9205)


We establish a setting for asynchronous stochastic tasks that account for episodes, rewards and responses, and, most especially, the computational complexity of the algorithm behind an agent solving a task. This is used to determine the difficulty of a task as the (logarithm of the) number of computational steps required to acquire an acceptable policy for the task, which includes the exploration of policies and their verification. We also analyse instance difficulty, task compositions and decompositions.


Task difficulty Task breadth Levin’s search Universal psychometrics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alpcan, T., Everitt, T., Hutter, M.: Can we measure the difficulty of an optimization problem? In: IEEE Information Theory Workshop (ITW) (2014)Google Scholar
  2. 2.
    Bentley, J.G.W., Bishop, P.G., van der Meulen, M.J.P.: An empirical exploration of the difficulty function. In: Heisel, M., Liggesmeyer, P., Wittmann, S. (eds.) SAFECOMP 2004. LNCS, vol. 3219, pp. 60–71. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  3. 3.
    Hernández-Orallo, J.: A computational definition of ‘consilience’. Philosophica 61, 901–920 (2000)Google Scholar
  4. 4.
    Hernández-Orallo, J.: Computational measures of information gain and reinforcement in inference processes. AI Communications 13(1), 49–50 (2000)Google Scholar
  5. 5.
    Hernández-Orallo, J.: Constructive reinforcement learning. International Journal of Intelligent Systems 15(3), 241–264 (2000)CrossRefGoogle Scholar
  6. 6.
    Hernández-Orallo, J.: On environment difficulty and discriminating power. Autonomous Agents and Multi-Agent Systems, 1–53 (2014).
  7. 7.
    Hernández-Orallo, J., Dowe, D.L.: Measuring universal intelligence: Towards an anytime intelligence test. Artificial Intelligence 174(18), 1508–1539 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hernández-Orallo, J., Dowe, D.L., Hernández-Lloreda, M.V.: Universal psychometrics: measuring cognitive abilities in the machine kingdom. Cognitive Systems Research 27, 50–74 (2014)Google Scholar
  9. 9.
    Hutter, M.: Universal Artificial Intelligence: Sequential Decisions based on Algorithmic Probability. Springer (2005)Google Scholar
  10. 10.
    Levin, L.A.: Universal sequential search problems. Problems of Information Transmission 9(3), 265–266 (1973)zbMATHGoogle Scholar
  11. 11.
    Li, M., Vitányi, P.: An introduction to Kolmogorov complexity and its applications, 3rd edn. Springer (2008)Google Scholar
  12. 12.
    Mayfield, J.E.: Minimal history, a theory of plausible explanation. Complexity 12(4), 48–53 (2007)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Schmidhuber, J.: Gödel machines: fully self-referential optimal universal self-improvers. In: Artificial general intelligence, pp. 199–226. Springer (2007)Google Scholar
  14. 14.
    Valiant, L.G.: A theory of the learnable. Communications of the ACM 27(11), 1134–1142 (1984)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.DSICUniversitat Politècnica de ValènciaValènciaSpain

Personalised recommendations