Active sequential hypothesis testing problem arises in a broad spectrum of applications in cognition, communications, design of experiments, and sensor management. In all of these applications, a decision maker is responsible to take actions dynamically so as to enhance information about an underlying phenomena of interest in a speedy manner while accounting for the cost of communication, sensing, or data collection. In particular, due to the sequential nature of the problem, the decision maker relies on his current information state to constantly (re-)evaluate the trade-off between the precision and the cost of various actions.
In this work, we first discuss active sequential hypothesis testing as a partially observable Markov decision problem. In particular, we provide a brief survey of the design of experiment literature and the dynamic programming interpretation of information utility introduced by De Groot. Using Blackwell ordering, we, then, connect this stochastic control theoretic notion of information utility to the concept of stochastic degradation and uncertainty reduction in information theory.
Finally, we discuss the dynamics and expected drift of log-likelihood, entropy, and probability of error as well as their connection to Kullback-Leibler divergence and mutual information in order to approximate the optimal value function (i.e. the solutions to the DP). We then utilize these value function approximations (lower bounds) to provide simple sequential test strategies (heuristics) whose performance is numerically compared to the optimal policies. Finally, we prove the asymptotic optimality of one class of these heuristic test strategies and, as a special case, recover Burnashev's coding scheme in the context of variable-length block coding over memoryless channels with feedback. Time permitting, we will compare and contrast our approach with recent results in Bayesian active learning literature (this is joint work with Mohammad Naghshvar and Ofer Shayevitz).
Bio: Tara Javidi studied electrical engineering at Sharif University of Technology, Tehran, Iran from 1992 to 1996. She received the MS degrees in electrical engineering (systems), and in applied mathematics (stochastics) from the University of Michigan, Ann Arbor, in 1998 and 1999, respectively. She received her Ph.D. in electrical engineering and computer science from the University of Michigan, Ann Arbor, in 2002.
From 2002 to 2004, she was an assistant professor at the Electrical Engineering Department, University of Washington, Seattle. She joined University of California, San Diego, in 2005, where she is currently an associate professor of electrical and computer engineering.
Tara Javidi was a Barbour Scholar during 1999-2000 academic year and received an NSF CAREER Award in 2004. Her research interests are in communication networks, stochastic resource allocation, stochastic control theory, and wireless communications.
