On computing optimal thresholds in decentralized sequential hypothesis testing

There has been a lot of recent progress in understanding the structure of optimal control strategies in decentralized stochastic control, but not much is known about computational methods. In this paper, we propose two finite-state approximation methods for decentralized sequential hypothesis testing. The first method, which is called orthogonal search, is an iterative method that approximately solves the coupled dynamic programs proposed in Teneketzis and Ho, Information and Computation, 1987. The second method, which is called direct search, approximates the performance of a threshold-based strategy and then searches over the thresholds using a derivative-free non-convex optimization algorithm. The approximations for both methods are based on the discretization of the information state process to a finite-state Markov chain, and calculating the absorption probabilities and absorption stopping times for appropriately defined absorption sets. The performance of both the methods is compared numerically.