We study the problem of optimizing the decisions of a preemptively capable transmitter to minimize the Age of Incorrect Information (AoII) when the communication channel has a random delay. We consider a slotted-time system where a transmitter observes a Markovian source and makes decisions based on the system status. In each time slot, the transmitter decides whether to preempt or skip when the channel is busy. When the channel is idle, the transmitter decides whether to send a new update. A remote receiver estimates the state of the Markovian source based on the update it receives. We consider a generic transmission delay and assume that the transmission delay is independent and identically distributed for each update. This paper aims to optimize the transmitter's decision in each time slot to minimize the AoII with generic time penalty functions. To this end, we first use the Markov decision process to formulate the optimization problem and derive the analytical expressions of the expected AoIIs achieved by two canonical preemptive policies. Then, we prove the existence of the optimal policy and provide a feasible value iteration algorithm to approximate the optimal policy. However, the value iteration algorithm will be computationally expensive if we want considerable confidence in the approximation. Therefore, we analyze the system characteristics under two canonical delay distributions and theoretically obtain the corresponding optimal policies using the policy improvement theorem. Finally, numerical results are presented to illustrate the performance improvements brought about by the preemption capability.

翻译：本文研究在通信信道存在随机延迟时，具有抢占能力的发射器如何优化决策以最小化错误信息年龄（Age of Incorrect Information, AoII）的问题。我们考虑一个时隙化系统，其中发射器观测马尔可夫源并根据系统状态做出决策。在每个时隙内，当信道繁忙时，发射器决定是进行抢占还是跳过；当信道空闲时，发射器决定是否发送新更新。远程接收器根据接收到的更新估计马尔可夫源的状态。本文考虑一般性传输延迟，并假设每次更新的传输延迟独立同分布。本文旨在优化每个时隙的发射器决策，以在采用通用时间惩罚函数时最小化AoII。为此，我们首先利用马尔可夫决策过程对优化问题进行建模，并推导两种典型抢占策略下预期AoII的解析表达式。接着，我们证明最优策略的存在性，并给出一种可行的值迭代算法来逼近最优策略。然而，若需要获得较高置信度的近似解，值迭代算法的计算成本将十分高昂。因此，我们分析两种典型延迟分布下的系统特征，并利用策略改进定理从理论上获得相应的最优策略。最后，通过数值结果展示抢占能力带来的性能提升。