15 research outputs found
Active Search with a Cost for Switching Actions
Active Sequential Hypothesis Testing (ASHT) is an extension of the classical
sequential hypothesis testing problem with controls. Chernoff (Ann. Math.
Statist., 1959) proposed a policy called Procedure A and showed its asymptotic
optimality as the cost of sampling was driven to zero. In this paper we study a
further extension where we introduce costs for switching of actions. We show
that a modification of Chernoff's Procedure A, one that we call Sluggish
Procedure A, is asymptotically optimal even with switching costs. The growth
rate of the total cost, as the probability of false detection is driven to
zero, and as a switching parameter of the Sluggish Procedure A is driven down
to zero, is the same as that without switching costs.Comment: 8 pages. Presented at 2015 Information Theory and Applications
Worksho
Quickest Change Detection with Controlled Sensing
In the problem of quickest change detection, a change occurs at some unknown
time in the distribution of a sequence of random vectors that are monitored in
real time, and the goal is to detect this change as quickly as possible subject
to a certain false alarm constraint. In this work we consider this problem in
the presence of parametric uncertainty in the post-change regime and controlled
sensing. That is, the post-change distribution contains an unknown parameter,
and the distribution of each observation, before and after the change, is
affected by a control action. In this context, in addition to a stopping rule
that determines the time at which it is declared that the change has occurred,
one also needs to determine a sequential control policy, which chooses the
control action at each time based on the already collected observations. We
formulate this problem mathematically using Lorden's minimax criterion, and
assuming that there are finitely many possible actions and post-change
parameter values. We then propose a specific procedure for this problem that
employs an adaptive CuSum statistic in which (i) the estimate of the parameter
is based on a fixed number of the more recent observations, and (ii) each
action is selected to maximize the Kullback-Leibler divergence of the next
observation based on the current parameter estimate, apart from a small number
of exploration times. We show that this procedure, which we call the Windowed
Chernoff-CuSum (WCC), is first-order asymptotically optimal under Lorden's
minimax criterion, for every possible possible value of the unknown post-change
parameter, as the mean time to false alarm goes to infinity. We also provide
simulation results to illustrate the performance of the WCC procedure
Active Anomaly Detection in Heterogeneous Processes
An active inference problem of detecting anomalies among heterogeneous
processes is considered. At each time, a subset of processes can be probed. The
objective is to design a sequential probing strategy that dynamically
determines which processes to observe at each time and when to terminate the
search so that the expected detection time is minimized under a constraint on
the probability of misclassifying any process. This problem falls into the
general setting of sequential design of experiments pioneered by Chernoff in
1959, in which a randomized strategy, referred to as the Chernoff test, was
proposed and shown to be asymptotically optimal as the error probability
approaches zero. For the problem considered in this paper, a low-complexity
deterministic test is shown to enjoy the same asymptotic optimality while
offering significantly better performance in the finite regime and faster
convergence to the optimal rate function, especially when the number of
processes is large. The computational complexity of the proposed test is also
of a significantly lower order.Comment: This work has been accepted for publication on IEEE Transactions on
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