Active Fixed-Sample-Size Hypothesis Testing Via POMDP Value Function Lipschitz Bounds

We establish the Lipschitz continuity of the value functions of an active fixed-sample-size hypothesis testing problem when it is reformulated as a partially observed Markov decision process. These Lipschitz results enable us to develop novel upper and lower bounds on the value of information, which is the expected difference between the value functions before and after performing an experiment. Our novel Lipschitz and value-of-information results provide new practical insight into optimal policies for active fixed-sample-size hypothesis testing without resorting to approximate dynamic programming schemes or asymptotic analysis with infinite numbers of samples. We illustrate the utility of our results by showing that a simple scheme based on selecting experiments that maximize a value-of-information bound achieves near-optimal performance in simulations.