Meeting Uncertain Threats with Feedback
arXiv:2607.13648
The paper models the rapid allocation of limited defensive resources against multiple uncertain threats as a Markov decision process and evaluates simple time‑oblivious policies, showing that fair allocation is optimal in homogeneous settings and that greedy, threat‑aware policies achieve near‑optimal performance with provable guarantees.
Abstract
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.