We study Bayesian persuasion under approximate best response, where the receiver may choose any action that is not too much suboptimal given their posterior belief upon receiving the signal. We focus on the computational aspects of the problem, aiming to design algorithms that efficiently compute (almost) optimal strategies for the sender. Despite the absence of the revelation principle -- which has been one of the most powerful tools in Bayesian persuasion -- we design polynomial-time exact algorithms for the problem when either the state space or the action space is small, as well as a quasi-polynomial-time approximation scheme (QPTAS) for the general problem. On the negative side, we show there is no polynomial-time exact algorithm for the general problem unless $\mathsf{P} = \mathsf{NP}$. Our results build on several new algorithmic ideas, which might be useful in other principal-agent problems where robustness is desired.

翻译：我们研究近似最优反应下的贝叶斯说服问题，其中接收者可能选择任何在收到信号后的后验信念下并非过于次优的行动。我们聚焦于该问题的计算方面，旨在设计能够高效计算发送者（近乎）最优策略的算法。尽管缺乏启示原则——这一直是贝叶斯说服中最强大的工具之一——我们仍针对状态空间或行动空间较小的情况，设计了多项式时间精确算法；针对一般问题，我们提出了拟多项式时间近似方案（QPTAS）。在反面结果方面，我们证明了除非 $\mathsf{P} = \mathsf{NP}$，否则一般问题不存在多项式时间精确算法。我们的结果建立在若干新的算法思想之上，这些思想可能对需要鲁棒性的其他委托-代理问题具有参考价值。