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One-armed bandit models with continuous and delayed responses

Author

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  • Xikui Wang
  • Mikelis G. Bickis

Abstract

One-armed bandit processes with continuous delayed responses are formulated as controlled stochastic processes following the Bayesian approach. It is shown that under some regularity conditions, a Gittins-like index exists which is the limit of a monotonic sequence of break-even values characterizing optimal initial selections of arms for finite horizon bandit processes. Furthermore, there is an optimal stopping solution when all observations on the unknown arm are complete. Results are illustrated with a bandit model having exponentially distributed responses, in which case the controlled stochastic process becomes a Markov decision process, the Gittins-like index is the Gittins index and the Gittins index strategy is optimal. Copyright Springer-Verlag 2003

Suggested Citation

  • Xikui Wang & Mikelis G. Bickis, 2003. "One-armed bandit models with continuous and delayed responses," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 209-219, November.
    • Handle: RePEc:spr:mathme:v:58:y:2003:i:2:p:209-219
    DOI: 10.1007/s001860300295
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    Cited by:

    1. You Liang & Xikui Wang & Yanqing Yi, 2013. "One-armed bandit process with a covariate," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 993-1006, October.

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