Skip to main content
Top

2015 | OriginalPaper | Chapter

8. Predictive Complexity for Games with Finite Outcome Spaces

Author : Yuri Kalnishkan

Published in: Measures of Complexity

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Predictive complexity is a generalization of Kolmogorov complexity motivated by an on-line prediction scenario. It quantifies the “unpredictability” of a sequence in a particular prediction environment. This chapter surveys key results on predictive complexity for games with finitely many outcomes. The issues of existence, non-existence, uniqueness, and linear inequalities are covered.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Literature
1.
go back to reference Blackwell, D., Girshick, M.A.: Theory of Games and Statistical Decisions. Wiley, New York (1954)MATH Blackwell, D., Girshick, M.A.: Theory of Games and Statistical Decisions. Wiley, New York (1954)MATH
2.
go back to reference Cesa-Bianchi, N., Lugosi, G.: Prediction, Learning, and Games. Cambridge University Press, Cambridge (2006)MATHCrossRef Cesa-Bianchi, N., Lugosi, G.: Prediction, Learning, and Games. Cambridge University Press, Cambridge (2006)MATHCrossRef
3.
go back to reference Feller, W.: An Introduction to Probability Theory and Its Applications, 3rd edn. Wiley, New York (1968)MATH Feller, W.: An Introduction to Probability Theory and Its Applications, 3rd edn. Wiley, New York (1968)MATH
4.
go back to reference Ghosh, M., Nandakumar, S.: Predictive complexity and generalized entropy rate of stationary ergodic processes. In: Bshouty, N.H., Stoltz, G., Vayatis, N., Zeugmann, T. (eds.) Algorithmic Learning Theory. Lecture Notes in Computer Science, vol. 7568, pp. 365–379. Springer, Berlin (2012)CrossRef Ghosh, M., Nandakumar, S.: Predictive complexity and generalized entropy rate of stationary ergodic processes. In: Bshouty, N.H., Stoltz, G., Vayatis, N., Zeugmann, T. (eds.) Algorithmic Learning Theory. Lecture Notes in Computer Science, vol. 7568, pp. 365–379. Springer, Berlin (2012)CrossRef
5.
go back to reference Kalnishkan, Y.: General linear relations among different types of predictive complexity. Theor. Comput. Sci. 271(1–2), 181–200 (2002)MATHMathSciNetCrossRef Kalnishkan, Y.: General linear relations among different types of predictive complexity. Theor. Comput. Sci. 271(1–2), 181–200 (2002)MATHMathSciNetCrossRef
6.
go back to reference Kalnishkan, Y., Vovk, V., Vyugin, M.V.: Generalised entropies and asymptotic complexities of languages. Inf. Comput. 237, 101–141 (2014)MATHMathSciNetCrossRef Kalnishkan, Y., Vovk, V., Vyugin, M.V.: Generalised entropies and asymptotic complexities of languages. Inf. Comput. 237, 101–141 (2014)MATHMathSciNetCrossRef
7.
go back to reference Kalnishkan, Y., Vovk, V., Vyugin, M.V.: A criterion for the existence of predictive complexity for binary games. In: Ben-David, S., Case, J., Maruoka, A. (eds.) Algorithmic Learning Theory, 15th International Conference, ALT 2004, Proceedings. Lecture Notes in Computer Science, vol. 3244, pp. 249–263. Springer, Berlin (2004) Kalnishkan, Y., Vovk, V., Vyugin, M.V.: A criterion for the existence of predictive complexity for binary games. In: Ben-David, S., Case, J., Maruoka, A. (eds.) Algorithmic Learning Theory, 15th International Conference, ALT 2004, Proceedings. Lecture Notes in Computer Science, vol. 3244, pp. 249–263. Springer, Berlin (2004)
8.
go back to reference Kalnishkan, Y., Vovk, V., Vyugin, M.V.: Loss functions, complexities, and the Legendre transformation. Theor. Comput. Sci. 313(2), 195–207 (2004)MATHMathSciNetCrossRef Kalnishkan, Y., Vovk, V., Vyugin, M.V.: Loss functions, complexities, and the Legendre transformation. Theor. Comput. Sci. 313(2), 195–207 (2004)MATHMathSciNetCrossRef
10.
go back to reference Kalnishkan, Y., Vyugin, M.V.: On the absence of predictive complexity for some games. In: Cesa-Bianchi, N., Numao, M., Reischuk, R. (eds.) Algorithmic Learning Theory, 13th International Conference, Proceedings. Lecture Notes in Artificial Intelligence, vol. 2533, pp. 164–172. Springer, Berlin (2002)CrossRef Kalnishkan, Y., Vyugin, M.V.: On the absence of predictive complexity for some games. In: Cesa-Bianchi, N., Numao, M., Reischuk, R. (eds.) Algorithmic Learning Theory, 13th International Conference, Proceedings. Lecture Notes in Artificial Intelligence, vol. 2533, pp. 164–172. Springer, Berlin (2002)CrossRef
11.
13.
go back to reference Li, M., Vitányi, P.: An Introduction to Kolmogorov Complexity and Its Applications, 3rd edn. Springer, Berlin (2008)MATHCrossRef Li, M., Vitányi, P.: An Introduction to Kolmogorov Complexity and Its Applications, 3rd edn. Springer, Berlin (2008)MATHCrossRef
14.
go back to reference Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)MATH Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)MATH
15.
go back to reference Vovk, V., Watkins, C.J.H.C.: Universal portfolio selection. In: Proceedings of the 11th Annual Conference on Computational Learning Theory, pp. 12–23. ACM Press (1998) Vovk, V., Watkins, C.J.H.C.: Universal portfolio selection. In: Proceedings of the 11th Annual Conference on Computational Learning Theory, pp. 12–23. ACM Press (1998)
18.
go back to reference Zvonkin, A.K., Levin, L.A.: The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms. Russ. Math. Surv. 25(6), 83–124 (1970)MATHMathSciNetCrossRef Zvonkin, A.K., Levin, L.A.: The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms. Russ. Math. Surv. 25(6), 83–124 (1970)MATHMathSciNetCrossRef
Metadata
Title
Predictive Complexity for Games with Finite Outcome Spaces
Author
Yuri Kalnishkan
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-21852-6_8

Premium Partner