1 research outputs found
Sequential Experiment Design for Hypothesis Verification
Hypothesis testing is an important problem with applications in target
localization, clinical trials etc. Many active hypothesis testing strategies
operate in two phases: an exploration phase and a verification phase. In the
exploration phase, selection of experiments is such that a moderate level of
confidence on the true hypothesis is achieved. Subsequent experiment design
aims at improving the confidence level on this hypothesis to the desired level.
In this paper, the focus is on the verification phase. A confidence measure is
defined and active hypothesis testing is formulated as a confidence
maximization problem in an infinite-horizon average-reward Partially Observable
Markov Decision Process (POMDP) setting. The problem of maximizing confidence
conditioned on a particular hypothesis is referred to as the hypothesis
verification problem. The relationship between hypothesis testing and
verification problems is established. The verification problem can be
formulated as a Markov Decision Process (MDP). Optimal solutions for the
verification MDP are characterized and a simple heuristic adaptive strategy for
verification is proposed based on a zero-sum game interpretation of
Kullback-Leibler divergences. It is demonstrated through numerical experiments
that the heuristic performs better in some scenarios compared to existing
methods in literature.Comment: 52nd Annual Asilomar Conference on Signals, Systems, and Computers.
arXiv admin note: text overlap with arXiv:1810.0485