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1 results

  • Optimal stopping and dynamic allocation

  • Fu Chang, Tze Leung Lai
  • Journal:
    Advances in Applied Probability / Volume 19 / Issue 4 / December 1987
    Published online by Cambridge University Press:
    01 July 2016, pp. 829-853
    Print publication:
    December 1987

  • A class of optimal stopping problems for the Wiener process is studied herein, and asymptotic expansions for the optimal stopping boundaries are derived. These results lead to a simple index-type class of asymptotically optimal solutions to the classical discounted multi-armed bandit problem: given a discount factor 0<β <1 and k populations with densities from an exponential family, how should x 1, x 2,… be sampled sequentially from these populations to maximize the expected value of Ʃ∞ 1 βi−1 x i , in ignorance of the parameters of the densities?