On Low-Complexity Quickest Intervention of Mutated Diffusion Processes Through Local Approximation

TL;DR

This paper develops low-complexity algorithms for quickly intervening in mutated diffusion processes, balancing intervention speed and cost, with applications in pandemic control and misinformation containment.

Contribution

It introduces a local approximation-based threshold policy for low-complexity intervention in mutated diffusion processes, improving computational efficiency over existing methods.

Findings

The low-complexity threshold policy performs comparably to grid approximation methods.

Both proposed algorithms outperform traditional QCD-based algorithms.

Simulation results validate the effectiveness of the local approximation approach.

Abstract

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.