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Targeting a Simple Statistical Bandit Problem

  • Antoine Chambaz
  • Wenjing Zheng
  • Mark J. van der Laan
Chapter
First Online:
Part of the Springer Series in Statistics book series (SSS)

Abstract

An infinite sequence of independent and identically distributed (i.i.d.) random variables (W n , Y n (0), Y n (1))n ≥ 1 drawn from a common law Q0 is to be sequentially and partially disclosed during the course of a controlled experiment. The first component, W n , describes the nth context in which we will have to carry out one action out of two, denoted a = 0 and a = 1. The second and third components, Y n (0) and Y n (1), are the rewards that actions a = 0 and a = 1 would grant. The set \(\mathcal{W}\) of contexts may be high-dimensional. The rewards take their values in ]0, 1[.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Antoine Chambaz
    • 1
  • Wenjing Zheng
    • 2
  • Mark J. van der Laan
    • 3
  1. 1.MAP5 (UMR CNRS 8145)Université Paris DescartesParis cedex 06France
  2. 2.NetflixLos GatosUSA
  3. 3.Division of Biostatistics and Department of StatisticsUniversity of California, BerkeleyBerkeleyUSA

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