AI 中文总结
研究在防空等领域面对不确定威胁时的防御分配问题，将其建模为马尔可夫决策过程，提出简单时间无关策略，如公平分配和考虑威胁难度的贪婪策略，分析各策略效果，为应对此类问题提供有效方法。
AI 中文摘要
防空与导弹防御、海军力量保护以及关键基础设施安全等领域，在中和不确定且仅在一轮射击后才能观测到时，需要快速将稀缺的效应器分配给多个来袭威胁。我们将此防御分配问题表述为马尔可夫决策过程，其中指挥官在三个作战目标下，每轮为异构威胁分配固定量的效应器能力：最小化预期威胁清除时间、最大化截止日期前清除的概率、最大化截止日期前的有效分配。我们研究适用于快速实施的简单时间无关策略，而非昂贵的完全动态优化。公平分配忽略威胁难度并均匀分配火力，在同质威胁或低能力交战下对所有三个目标都是最优的。此外，当效应器能力至少与威胁数量成线性比例时，其威胁清除时间最多比最优策略落后常数轮数。我们还为每个目标开发了考虑威胁难度的贪婪策略，包括有效分配最大化的常数因子保证。数值上，贪婪策略在异构实例中接近最优，而当威胁难度未知时，公平分配仍然是一个有原则的选择。
英文摘要
Air and missile defense, naval force protection, and critical-infrastructure security require rapid allocation of scarce effectors against multiple incoming threats when neutralization is uncertain and observed only after a firing round. We formulate this defensive-allocation problem as a Markov decision process in which a commander assigns a fixed amount of effector capacity each round to heterogeneous threats under three operational objectives: minimizing expected threat-clearance time, maximizing the probability of clearance by a deadline, and maximizing effective assignments before a deadline. Rather than expensive full dynamic optimization, we study simple time-oblivious policies suited to fast implementation. Fair allocation, which ignores threat difficulty and spreads fire evenly, is highly effective: it is optimal for all three objectives under homogeneous threats or low-capacity engagements. Moreover, when effector capacity scales at least linearly with the number of threats, its threat-clearance time trails that of the optimal policy by at most a constant number of rounds. We further develop threat-difficulty-aware greedy policies for each objective, including a constant-factor guarantee for effective assignment maximization. Numerically, greedy policies are near-optimal across heterogeneous instances, while fair allocation remains a principled choice when threat difficulties are unknown.
