We study a repeated information design problem faced by an informed sender
who tries to influence the behavior of a self-interested receiver. We consider
settings where the receiver faces a sequential decision making (SDM) problem.
At each round, the sender observes the realizations of random events in the SDM
problem. This begets the challenge of how to incrementally disclose such
information to the receiver to persuade them to follow (desirable) action
recommendations. We study the case in which the sender does not know random
events probabilities, and, thus, they have to gradually learn them while
persuading the receiver. We start by providing a non-trivial polytopal
approximation of the set of sender's persuasive information structures. This is
crucial to design efficient learning algorithms. Next, we prove a negative
result: no learning algorithm can be persuasive. Thus, we relax persuasiveness
requirements by focusing on algorithms that guarantee that the receiver's
regret in following recommendations grows sub-linearly. In the full-feedback
setting -- where the sender observes all random events realizations -- , we
provide an algorithm with $\tilde{O}(\sqrt{T})$ regret for both the sender and
the receiver. Instead, in the bandit-feedback setting -- where the sender only
observes the realizations of random events actually occurring in the SDM
problem -- , we design an algorithm that, given an $\alpha \in [1/2, 1]$ as
input, ensures $\tilde{O}({T^\alpha})$ and $\tilde{O}( T^{\max \{ \alpha,
1-\frac{\alpha}{2} \} })$ regrets, for the sender and the receiver
respectively. This result is complemented by a lower bound showing that such a
regrets trade-off is essentially tight.

研究了在信息设计问题中，如何让一个自利的决策人在面对连续决策时遵循某些规则，并提出了相应的学习算法，该算法可以保证提示者和接收者在不同条件下的回报。