Parametrized design of the generalized sequential probability ratio test
A generalized sequential probability ratio test (GSPRT) is a classical algorithm for binary sequential hypothesis testing. Though it is well-studied in the literature, there has been no optimal design of this test due to the difficulty of choosing its thresholds. In this paper we formulate the binary sequential hypothesis testing as an optimization problem. The latter is non-convex, and finding a global minimizer of the objective is combinatorially complex in the number of stages of the sequential test. On the other hand, greedily minimizing the objective has linear complexity but achieves sub-optimal results. We propose a generalization of the greedy approach that allows the designer to trade off complexity for closeness of the thresholds to their optimal values. Simulation results show that the proposed method gives arbitrarily close solution to optimal by increasing the window span of future sample distributions that are utilized to set a current test threshold. The window span is a hyper-parameter that is optimized for the target application.