Metrika

, Volume 32, Issue 1, pp 395–407 | Cite as

On monotone optimal decision rules and the stay-on-a-winner rule for the two-armed bandit

  • M. Kolonko
  • H. Benzing
Publication

Summary

Consider the following optimization problem: Find a decision rule δ such thatw(x, δ (x))=max a w(x, a) for allx under the constraint δ (x)∈D (x). We give conditions for the existence of monotone optimal decision rules δ. The term ‘monotone’ is used in a general sense. The well-known stay-on-a-winner rules for the two-armed bandit can be characterized as monotone decision rules by including the stage number intox and using a special ordering onx. This enables us to give simple conditions for the existence of optimal rules that are stay-on-a-winner rules. We extend results ofBerry andKalin/Theodorescu to the case of dependent arms.

Keywords

Stochastic Process Probability Theory Economic Theory Decision Rule General Sense 

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Copyright information

© Physica-Verlag Ges.m.b.H. 1985

Authors and Affiliations

  • M. Kolonko
    • 1
  • H. Benzing
    • 1
  1. 1.Institut für Mathematische Statistik der Universität KarlsruheKarlsruhe 1Germany

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