Active hypothesis testing: Sequentiality and adaptivity gains

Consider a decision maker who is responsible to collect observations so as to enhance his information in a speedy manner about an underlying phenomena of interest. The policies under which the decision maker selects sensing actions can be categorized based on the following two factors: i) sequential vs. non-sequential; ii) adaptive vs. non-adaptive. Non-sequential policies collect a fixed number of observation samples and make the final decision afterwards; while under sequential policies, the sample size is not known initially and is determined by the observation outcomes. Under adaptive policies, the decision maker relies on the previous collected samples to select the next sensing action; while under non-adaptive policies, the actions are selected independent of the past observation outcomes. In this paper, performance bounds are provided for the policies in each category. Using these bounds, sequentiality gain and adaptivity gain, i.e., the gains of sequential and adaptive selection of actions are characterized.

[1]  Pravin Varaiya,et al.  Stochastic Systems: Estimation, Identification, and Adaptive Control , 1986 .

[2]  Venkatesh Saligrama,et al.  Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[3]  D. Blackwell.  Equivalent Comparisons of Experiments , 1953 .

[4]  M. Iwen.  Group testing strategies for recovery of sparse signals in noise , 2009, 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers.

[5]  Colin McDiarmid,et al.  Surveys in Combinatorics, 1989: On the method of bounded differences , 1989 .

[6]  Alfred O. Hero,et al.  Sensor Management: Past, Present, and Future , 2011, IEEE Sensors Journal.

[7]  J. Norris.  Appendix: probability and measure , 1997 .

[8]  Urbashi Mitra,et al.  Parametric Methods for Anomaly Detection in Aggregate Traffic , 2011, IEEE/ACM Transactions on Networking.

[9]  Pradeep Shenoy,et al.  Rational Decision-Making in Inhibitory Control , 2011, Front. Hum. Neurosci..

[10]  Tara Javidi,et al.  Performance bounds for active sequential hypothesis testing , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[11]  Matthew Malloy,et al.  Sequential analysis in high-dimensional multiple testing and sparse recovery , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[12]  Geoffrey A. Hollinger,et al.  Active Classification: Theory and Application to Underwater Inspection , 2011, ISRR.

[13]  M. V. Burnašev.  SEQUENTIAL DISCRIMINATION OF HYPOTHESES WITH CONTROL OF OBSERVATIONS , 1980 .

[14]  Richard E. Blahut,et al.  Hypothesis testing and information theory , 1974, IEEE Trans. Inf. Theory.

[15]  Tara Javidi,et al.  Active Sequential Hypothesis Testing , 2012, ArXiv.

[16]  V. Bentkus,et al.  An extension of the Hoeffding inequality to unbounded random variables , 2008 .