Two-armed Bandit Problem and Nonlinear Limit Theorems

  • [2020-11-04]

    Speaker:  CHEN Zengjing

                     Shandong University

    Time: 2020-11-04, 16:00

    Place (virtual): Zoom ID 99854631775, Password 123456

    Organizer: School of Mathematical Sciences



    In this paper we introduce and study a Bernoulli-like model in the context of nonlinear probabilities, which we call the binary uncertainty model. This work is motivated mainly from the “two-armed bandit” problem. Our model provides a new way to study the “two-armed bandit” problem and, more generally, the distribution uncertainties. In one main result we obtain the central limit theorem for this model, and give an explicit formula for the limit distribution. The limit is shown to depend heavily on the structure of the events or the integrating functions, which demonstrate the key signature of nonlinear structure. We also establish the large deviation principle and, as an application, derive the weak law of large numbers. The large deviation rate function is identified explicitly. These limit theorems provide the theoretical foundation for statistical inferences.



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