变异扩散过程的低复杂性局部逼近最快干预
On Low-Complexity Quickest Intervention of Mutated Diffusion Processes Through Local Approximation
摘要：
研究了具有未知变异时间的变异扩散过程的控制问题。该问题被表述为最快干预问题，其变异由变点建模，这是最快变点检测（QCD）的推广。我们的目标是尽快干预突变过程，同时保持低干预成本，最佳选择的干预行动。该模型和所提出的算法可应用于大流行预防（如Covid-19）或错误信息遏制。我们制定的问题作为一个部分可观察的马尔可夫决策过程（POMDP），并将其转换为MDP通过信念状态的变化点。首先，我们提出了一个网格近似的方法来计算最优的干预政策，其计算复杂度可能是非常高的网格数时，很大。为了降低计算复杂度，我们进一步提出了一个低复杂度的阈值为基础的政策，通过分析的一阶近似值函数的“本地干预”制度。仿真结果表明，低复杂度的算法具有类似的性能的网格近似，都比基于QCD算法的性能要好得多。
英文摘要：
We consider the problem of controlling a mutated diffusion process with an unknown mutation time. The problem is formulated as the quickest intervention problem with the mutation modeled by a change-point, which is a generalization of the quickest change-point detection (QCD). Our goal is to intervene in the mutated process as soon as possible while maintaining a low intervention cost with optimally chosen intervention actions. This model and the proposed algorithms can be applied to pandemic prevention (such as Covid-19) or misinformation containment. We formulate the problem as a partially observed Markov decision process (POMDP) and convert it to an MDP through the belief state of the change-point. We first propose a grid approximation approach to calculate the optimal intervention policy, whose computational complexity could be very high when the number of grids is large. In order to reduce the computational complexity, we further propose a low-complexity threshold-based policy through the analysis of the first-order approximation of the value functions in the ``local intervention'' regime. Simulation results show the low-complexity algorithm has a similar performance as the grid approximation and both perform much better than the QCD-based algorithms.
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