Information Design with Unknown Prior

Information designers, such as online platforms, often do not know the beliefs of their receivers. We design learning algorithms so that the information designer can learn the receivers' prior belief from their actions through repeated interactions. Our learning algorithms achieve no regret relative to the optimality for the known prior at a fast speed, achieving a tight regret bound $\Theta(\log T)$ in general and a tight regret bound $\Theta(\log \log T)$ in the important special case of binary actions.