Bayesian Sequential Detection with Phase-Distributed Change Time and Nonlinear Penalty -- A POMDP Approach

Details Bayesian Sequential Detection with Phase-Distributed Change Time and Nonlinear Penalty -- A POMDP Approach Bayesian Sequential Detection with Phase-Distributed Change Time and Nonlinear Penalty -- A POMDP Approach

2010-11-24

arxiv.org/abs/1011.5298v4

IEEE Transactions Information Theory, October 2011. Vol.57, No.10

Computer Science

Information Theory

accepted for publication in IEEE Transactions Information Theory, 2011

Scientific paper

We show that the optimal decision policy for several types of Bayesian sequential detection problems has a threshold switching curve structure on the space of posterior distributions. This is established by using lattice programming and stochastic orders in a partially observed Markov decision process (POMDP) framework. A stochastic gradient algorithm is presented to estimate the optimal linear approximation to this threshold curve. We illustrate these results by first considering quickest time detection with phase-type distributed change time and a variance stopping penalty. Then it is proved that the threshold switching curve also arises in several other Bayesian decision problems such as quickest transient detection, exponential delay (risk-sensitive) penalties, stopping time problems in social learning, and multi-agent scheduling in a changing world. Using Blackwell dominance, it is shown that for dynamic decision making problems, the optimal decision policy is lower bounded by a myopic policy. Finally, it is shown how the achievable cost of the optimal decision policy varies with change time distribution by imposing a partial order on transition matrices.

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