A Control Problem Arising in the Sequential Design of Experiments

Lalley, Steven P.; Lorden, G.

doi:10.1214/aop/1176992620

Cited by 25 publications

(15 citation statements)

References 11 publications

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“…When we do not possess complete knowledge of the system, these two objectives may be in conflict, giving rise to the so-called dual effect of control [7]. With the exception of experimental design [8], [9] (and, in particular, some work connecting it with control [10], [11]), statistical estimation involves passively observing sample paths of a random process for the purpose of inference. Our Meta-Theorem covers both estimation and control, since the former can be viewed as an application of a control strategy that has no effect on the system, and it provides a way of quantifying the dual effect in the latter.…”

Section: Introductionmentioning

confidence: 99%

Divergence-based characterization of fundamental limitations of adaptive dynamical systems

Raginsky

2010

2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount importance. In this paper, we consider the general problem of adaptively controlling and/or identifying a stochastic dynamical system, where our a priori knowledge allows us to place the system in a subset of a metric space (the uncertainty set). We present an information-theoretic meta-theorem that captures the trade-off between the metric complexity (or richness) of the uncertainty set, the amount of information acquired online in the process of controlling and observing the system, and the residual uncertainty remaining after the observations have been collected. Following the approach of Zames, we quantify a priori information by the Kolmogorov (metric) entropy of the uncertainty set, while the information acquired online is expressed as a sum of information divergences. The general theory is used to derive new minimax lower bounds on the metric identification error, as well as to give a simple derivation of the minimum time needed to stabilize an uncertain stochastic linear system.

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Section: Introductionmentioning

confidence: 99%

Divergence-based characterization of fundamental limitations of adaptive dynamical systems

Raginsky

2010

2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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“…When these limits exist, the LLRs can be considered as random walks with variable step sizes, and the limit terms in (41) imply that the fluctuations in the average step sizes are diminishing as |U | grows. We note that the limits in (41) converge completely if and only if E {T (h)} < ∞ for all h ∈ (0, 1), where…”

Section: Delay Analysismentioning

confidence: 99%

“…The proposed selection rule, under each hypothesis H , identifies the subsequence of nodes that achieves the largest values for I in (41) and, since the average delay is inversely proportional to I , it also minimizes the average delay.…”

Section: Delay Analysismentioning

confidence: 99%

“…, Y n } are drawn from distribution f 0 . This is equivalent to the definition of I 0 provided in (41…”

Section: G Proof Of Theoremmentioning

confidence: 99%

“…In pioneering studies, [39] and [40] offer a strategy that initially takes a number of measurements according to a pre-designated rule in order to identify the true hypothesis, after which it selects the action that maximizes the information under the identified hypothesis. The study in [41] proposes a heuristic strategy and characterizes the deviation of its average delay from the optimal rule. Recently, more studies have investigated the Bayesian setting [42,43,44,45,46].…”

Section: Introductionmentioning

confidence: 99%

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Quickest detection of Markov networks

Heydari

Tajer

Poor

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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Detecting correlation structures in large networks arises in many domains. Such detection problems are often studied independently of the underlying data acquisition process, rendering settings in which data acquisition policies (e.g., the sample-size) are pre-specified. Motivated by the advantages of data-adaptive sampling, this paper treats the inherently coupled problems of data acquisition and decision-making for correlation detection. Specifically, this paper considers a Markov network of agents generating random variables, and designs a sequential strategy for discerning the correlation model governing the Markov network. By abstracting the Markov network as an undirected graph, designing the quickest sampling strategy becomes equivalent to sequentially and data-adaptively identifying and sampling a sequence of vertices in the graph. Designing such coupled sensing and inference mechanisms is closely related to the notion of controlled sensing. The paper establishes that the known controlled sensing approaches, inspired by Chernoff's rule for controlled sensing, are not optimal in the context of the problem studied, and devises alternative information measures based on which optimal sensing and inference rules are characterized. Performance analyses and numerical evaluations demonstrate the gains of the proposed sequential approach over the existing fixedsample size and sequential approaches.

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1996

Sequential Stochastic Optimization

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A Control Problem Arising in the Sequential Design of Experiments

Cited by 25 publications

References 11 publications

Divergence-based characterization of fundamental limitations of adaptive dynamical systems

Divergence-based characterization of fundamental limitations of adaptive dynamical systems

Quickest detection of Markov networks

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