Index policies for discounted bandit problems with availability constraints

Savas Dayanik, Warren Buckler Powell, Kazutoshi Yamazaki

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


A multiarmed bandit problem is studied when the arms are not always available. The arms are first assumed to be intermittently available with some state/action-dependent probabilities. It is proven that no index policy can attain the maximum expected total discounted reward in every instance of that problem. The Whittle index policy is derived, and its properties are studied. Then it is assumed that the arms may break down, but repair is an option at some cost, and the new Whittle index policy is derived. Both problems are indexable. The proposed index policies cannot be dominated by any other index policy over all multiarmed bandit problems considered here. Whittle indices are evaluated for Bernoulli arms with unknown success probabilities.

Original languageEnglish (US)
Pages (from-to)377-400
Number of pages24
JournalAdvances in Applied Probability
Issue number2
StatePublished - Jun 2008

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Applied Mathematics


  • Gittins index
  • Multiarmed bandit problem
  • Optimal resource allocation
  • Restart-in problem
  • Whittle index


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