Data-Efficient Quickest Change Detection with On–Off Observation Control

Abstract

In this paper we extend the Shiryaev's quickest change detection formulation by also accounting for the cost of observations used before the change point. The observation cost is captured through the average number of observations used in the detection process before the change occurs. The objective is to select an on-off observation control policy, that decides whether or not to take a given observation, along with the stopping time at which the change is declared, so as to minimize the average detection delay, subject to constraints on both the probability of false alarm and the observation cost. By considering a Lagrangian relaxation of the constraint problem, and using dynamic programming arguments, we obtain an a posteriori probability based two-threshold algorithm that is a generalized version of the classical Shiryaev algorithm. We provide an asymptotic analysis of the two-threshold algorithm and show that the algorithm is asymptotically optimal, i.e., the performance of the two-threshold algorithm approaches that of the Shiryaev algorithm, for a fixed observation cost, as the probability of false alarm goes to zero. We also show, using simulations, that the two-threshold algorithm has good observation cost-delay trade-off curves, and provides significant reduction in observation cost as compared to the naive approach of fractional sampling, where samples are skipped randomly. Our analysis reveals that, for practical choices of constraints, the two thresholds can be set independent of each other: one based on the constraint of false alarm and another based on the observation cost constraint alone.

Optimal DoS attacks on Bayesian quickest change detection

“…Equation (12) can be obtained in a similar way to [7] (Page 103), as τ * C is also a stopping rules w.r.t. F k (though not the optimal one).…”

“…As there is no analytic expression of the optimal policy, it is impossible to obtain the accurate asymptotic behavior of the optimal DoS attack. Motivated by [12], [13], the asymptotic upper and lower bounds of EDD are established in the following theorem. Theorem 3.5: If N is finite, as ξ → ∞,…”

“…The solution is given numerically. Banerjee et al [12] studied the same problem but for only one sensor with on-off observation control. The analytically asymptotic properties of the two thresholds structure, which are not optimal but with low complexity, are given.…”

Data-efficient quickest change detection in distributed and multi-channel systems

“…In [9] and [10] we extended the classical quickest change detection formulations studied in [1], [2] and [3], by putting an additional constraint on the cost of observations used in the detection process. We proposed problem formulations, for the Bayesian setting in [9], and for two minimax settings in [10], in which the objective was to minimize some version of the average delay, subject to constraints on the false alarm rate and a version of the average number of observations taken before the change point.…”

“…We proposed problem formulations, for the Bayesian setting in [9], and for two minimax settings in [10], in which the objective was to minimize some version of the average delay, subject to constraints on the false alarm rate and a version of the average number of observations taken before the change point. For the i.i.d.…”