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1 results

  • A confirmation of a conjecture on Feldman’s two-armed bandit problem

  • Part of
  • Zengjing Chen, Yiwei Lin, Jichen Zhang
  • Journal:
    Journal of Applied Probability / Volume 61 / Issue 1 / March 2024
    Published online by Cambridge University Press:
    26 May 2023, pp. 121-136
    Print publication:
    March 2024
    • Article
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  • The myopic strategy is one of the most important strategies when studying bandit problems. In 2018, Nouiehed and Ross put forward a conjecture about Feldman’s bandit problem (J. Appl. Prob. (2018) 55, 318–324). They proposed that for Bernoulli two-armed bandit problems, the myopic strategy stochastically maximizes the number of wins. In this paper we consider the two-armed bandit problem with more general distributions and utility functions. We confirm this conjecture by proving a stronger result: if the agent playing the bandit has a general utility function, the myopic strategy is still optimal if and only if this utility function satisfies reasonable conditions.