报告地点： 腾讯会议：512-562-169

会议链接： https://meeting.tencent.com/dm/xN7y9v07hZmS

In this talk, we will introduce 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.