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Interactive model building for Q-learning

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  • Eric B. Laber
  • Kristin A. Linn
  • Leonard A. Stefanski

Abstract

Evidence-based rules for optimal treatment allocation are key components in the quest for efficient, effective health-care delivery. Q-learning, an approximate dynamic programming algorithm, is a popular method for estimating optimal sequential decision rules from data. Q-learning requires the modelling of nonsmooth, nonmonotone transformations of the data, complicating the search for adequately expressive, yet parsimonious, statistical models. The default Q-learning working model is multiple linear regression, which not only is misspecified under most data-generating models but also results in nonregular regression estimators, complicating inference. We propose an alternative strategy for estimating optimal sequential decision rules for which the requisite statistical modelling does not depend on nonsmooth, nonmonotone transformed data, does not result in nonregular regression estimators, is consistent under more data-generation models than is Q-learning, results in estimated sequential decision rules that have better sampling properties, and is amenable to established statistical methods for exploratory data analysis, model building and validation. We derive the new method, IQ-learning, via an interchange in the order of certain steps in Q-learning. In simulated experiments, IQ-learning improves upon Q-learning in terms of integrated mean-squared error and power. The method is illustrated using data from a study of major depressive disorder.

Suggested Citation

  • Eric B. Laber & Kristin A. Linn & Leonard A. Stefanski, 2014. "Interactive model building for Q-learning," Biometrika, Biometrika Trust, vol. 101(4), pages 831-847.
  • Handle: RePEc:oup:biomet:v:101:y:2014:i:4:p:831-847.
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    File URL: http://hdl.handle.net/10.1093/biomet/asu043
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    Cited by:

    1. Xin Qiu & Donglin Zeng & Yuanjia Wang, 2018. "Estimation and evaluation of linear individualized treatment rules to guarantee performance," Biometrics, The International Biometric Society, vol. 74(2), pages 517-528, June.
    2. Emily L. Butler & Eric B. Laber & Sonia M. Davis & Michael R. Kosorok, 2018. "Incorporating Patient Preferences into Estimation of Optimal Individualized Treatment Rules," Biometrics, The International Biometric Society, vol. 74(1), pages 18-26, March.
    3. Kristin A. Linn & Eric B. Laber & Leonard A. Stefanski, 2017. "Interactive -Learning for Quantiles," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 638-649, April.
    4. Qian Guan & Eric B. Laber & Brian J. Reich, 2016. "Comment," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 936-942, July.
    5. Yuqian Zhang & Weijie Ji & Jelena Bradic, 2021. "Dynamic treatment effects: high-dimensional inference under model misspecification," Papers 2111.06818, arXiv.org, revised Jun 2023.

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