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One-armed bandit process with a covariate

Author

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  • You Liang
  • Xikui Wang
  • Yanqing Yi

Abstract

We generalize the bandit process with a covariate introduced by Woodroofe in several significant directions: a linear regression model characterizing the unknown arm, an unknown variance for regression residuals and general discounting sequence for a non-stationary model. With the Bayesian regression approach, we assume a normal-gamma conjugate prior distribution of the unknown parameters. It is shown that the optimal strategy is determined by a sequence of index values which are monotonic and determined by the observed value of the covariate and updated posterior distributions. We further show that the myopic strategy is not optimal in general. Such structural properties help to understand the tradeoff between information gathering and immediate expected payoff and may provide certain insight for covariate adjusted response adaptive design of clinical trials. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:5:p:993-1006
    DOI: 10.1007/s10463-013-0401-5
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    References listed on IDEAS

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    1. Xikui Wang & Yan Wang, 2010. "Optimal investment and consumption with stochastic dividends," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(6), pages 792-808, November.
    2. 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.
    3. Wang, Xikui, 2000. "A bandit process with delayed responses," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 303-307, July.
    4. Xikui Wang & Yanqing Yi, 2009. "An optimal investment and consumption model with stochastic returns," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(1), pages 45-55, January.
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