Regret Based Bayesian Sequential Experiment Design for Sensor Management

Measurement design is an important sub-problem arising in the applications of sensing and wireless communications. Sensing systems are often capable of performing different types of mutually exclusive measurement actions. In such systems, it is important to select measurement actions so as to efficiently gather samples which are most informative about the phenomena of interest. Bayesian sequential experiment design (BSED) offers a model-based framework with which to address sequential variations of such measurement design problems. Prior applications of BSED to sensing problems often consider measurement selection policies which maximize notions of expected information gain (EIG). In certain related settings, EIG based approaches have been shown to be less performant than policies designed to minimize notions of regret with respect to the information gain afforded by an ideal policy. Motivate by this, we develop a general framework based on partially observable Markov decision processes which allows for the design of BSED policies with respect to a notion of regret. We argue for the consideration of policies based on a myopic version of posterior sampling, termed MPS, and consider the application of this framework to the problem of passive non-coherent signal source localization and detection using codebook-based receive beamforming. We further develop a general approach for approximating posterior inference based on variational inference and a power law generalization of Bayes’ rule. We conduct an empirical analysis of the application of MPS and EIG to our considered application. Our results indicate that MPS outperforms EIG while providing improved robustness.