Skip to main content

Gittins Type Index Theorem for Randomly Evolving Graphs

  • Chapter

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berry, D.A., Fristedt, B.: Bandit problems. Sequential Allocation of Experi-ments. Monographs on Statistics and Applied Probability. Chapman & Hall, London (1985)

    Google Scholar 

  2. Bellman, R.: A problem in the sequential design of experiments. Sankhya 16, 221-229 (1956)

    MATH  MathSciNet  Google Scholar 

  3. Denardo, E.V., Rothblum, U.G., Van der Heyden, L.: Index policies for stochas-tic search in a forest with an application to R&D project management. Math. Oper. Res. 29, no. 1, 162-181 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Feldman, D.: Contributions to the “two-armed bandit” problem. Ann. Math. Statist. 33, 847-856 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  5. Feinberg E., Schwartz A. (eds): Handbook of Markov Decision Processes. Kluwer Acad. Publ. (2002)

    Google Scholar 

  6. Gittins, J. C.: A Multi-armed Bandit Allocation indices. Wiley , Ney York (1989)

    MATH  Google Scholar 

  7. Gittins, J.C., Jones, D.M.: A dynamic allocation index for the sequential design experiments. In: Gani, J., Sarkadi, K., Vince, I. (eds) Progress in Statistics, Eu-ropean Meeting of Statisticians I. North Holland, Amsterdam, 241-266 (1974).

    Google Scholar 

  8. Granot, D., Zuckerman, D.,: Optimal sequencing and resource allocation in re-search and development projects. Management Science 37, 140-156 (1991)

    Article  MATH  Google Scholar 

  9. Mitten, L.G.: An analytic solution to the least cost testing sequence problem. J. of Industr. Eng., 11, no. 1, 17 (1960)

    Google Scholar 

  10. Presman, E.L., Sonin, I.M.: Sequential Control with Incomplete Information. The Bayesian Approach to Multi-armed Bandit Problems. Academic Press (1990)

    Google Scholar 

  11. Sonin, I.M.: Increasing the reliability of a machine reduces the period of its work. J. Appl. Probab. 33, no. 1, 217-223 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  12. Sonin, I.M.: A Generalized Gittins index for Markov chain and its recursive calculation. Manuscript (2004)

    Google Scholar 

  13. Varaiya, P., Walrand J., Buyukkoc, C.: Extensions of the multiarmed bandit problem: the discounted case. IEEE Trans. Autom. Control AC-30, no. 5, 426-439(1985)

    Article  MathSciNet  Google Scholar 

  14. Weiss, G.: Branching bandit processes. Probability in the Engineering and In-formation Sciences 2, 269-278 (1988)

    Article  MATH  Google Scholar 

  15. Whittle, P.: Arm-acquiring bandits. Annals of Probability 9, 284-292 (1981)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Presman, E., Sonin, I. (2006). Gittins Type Index Theorem for Randomly Evolving Graphs. In: From Stochastic Calculus to Mathematical Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30788-4_28

Download citation

Publish with us

Policies and ethics