Bayesian persuasion studies how an informed sender should influence beliefs of rational receivers who take decisions through Bayesian updating of a common prior. We focus on the online Bayesian persuasion framework, in which the sender repeatedly faces one or more receivers with unknown and adversarially selected types. First, we show how to obtain a tight $\tilde O(T^{1/2})$ regret bound in the case in which the sender faces a single receiver and has partial feedback, improving over the best previously known bound of $\tilde O(T^{4/5})$. Then, we provide the first no-regret guarantees for the multi-receiver setting under partial feedback. Finally, we show how to design no-regret algorithms with polynomial per-iteration running time by exploiting type reporting, thereby circumventing known intractability results on online Bayesian persuasion. We provide efficient algorithms guaranteeing a $O(T^{1/2})$ regret upper bound both in the single- and multi-receiver scenario when type reporting is allowed.
