Optimal few-stage designs

Hardwick, Janis; Stout, Quentin F.

doi:10.1016/s0378-3758(01)00242-7

Cited by 32 publications

(25 citation statements)

References 24 publications

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“…That is, given utility at stage , is the random variable representing the optimal time to stop. That is: (12) Define as the optimal stopping time for the two-dimensional problem starting at stage with utilities , so that:…”

Section: Proof: Fixmentioning

confidence: 99%

“…This decision depends on the amount and quality of the information the sensors have already gathered at the decision instant. While the exploration-exploitation tradeoff has previously been studied for various wireless network scenarios, e.g., cognitive spectrum access [8], [9], autonomous resource management [10], and QoS routing [11], in this paper we specifically address the problem of adaptive sampling [12], [13] which focuses on the determination of the time to report sampled data. The proposed adaptive sampling algorithms attempt to maximize time average QoI-minus-cost.…”

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confidence: 99%

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Maximizing Quality of Information From Multiple Sensor Devices: The Exploration vs Exploitation Tradeoff

Ciftcioglu

Yener

Neely

2013

IEEE J. Sel. Top. Signal Process.

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Abstract-This paper investigates Quality of Information (QoI) aware adaptive sampling in a system where two sensor devices report information to an end user. The system carries out a sequence of tasks, where each task relates to a random event that must be observed. The accumulated information obtained from the sensor devices is reported once per task to a higher layer application at the end user. The utility of each report depends on the timeliness of the report and also on the quality of the observations. Quality can be improved by accumulating more observations for the same task, at the expense of delay. We assume new tasks arrive randomly, and the qualities of each new observation are also random. The goal is to maximize time average quality of information subject to cost constraints. We solve the problem by leveraging dynamic programming and Lyapunov optimization. Our algorithms involve solving a 2-dimensional optimal stopping problem, and result in a 2-dimensional threshold rule. When task arrivals are i.i.d., the optimal solution to the stopping problem can be closely approximated with a small number of simplified value iterations. When task arrivals are periodic, we derive a structured form approximately optimal stopping policy. We also introduce hybrid policies applied over the proposed adaptive sampling algorithms to further improve the performance. Numerical results demonstrate that our policies perform near optimal. Overall, this work provides new insights into network operation based on QoI attributes.Index Terms-Approximate dynamic programming, network utility maximization, quality of information.

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Section: Proof: Fixmentioning

confidence: 99%

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confidence: 99%

Maximizing Quality of Information From Multiple Sensor Devices: The Exploration vs Exploitation Tradeoff

Ciftcioglu

Yener

Neely

2013

IEEE J. Sel. Top. Signal Process.

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“…Many multistage designs, such as those in [2,8], are constrained to have a fixed number of stages. Instead we specify a maximum number of stages and let the final number be determined by the optimization process.…”

Section: ¥ Smentioning

confidence: 99%

“…For many applications the most important use of this may be the optimization of 2-or 3-stage designs where the size of each stage is allowed to depend on the outcomes observed previously. Such optimizations appeared in [2] in a more complex setting, though there was no incorporation of sampling costs nor early stopping. Even with just 2 stages, response adaptive stage sizes can provide useful improvements (Table 2).…”

Section: Final Commentsmentioning

confidence: 99%

Optimal screening designs with flexible cost and constraint structures

Stout

Hardwick

2005

Journal of Statistical Planning and Inference

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We describe a cost-and constraint-based decision-theoretic approach to the design of screening trials, where the goal is to identify promising candidates for future study or to decide whether to accept or reject a product. An algorithmic method for optimizing this approach is presented. This method utilizes a highly flexible structure to reflect a variety of decision and experimental costs and constraints. The designs produced can range from being a single stage up to being fully sequential, depending on the sampling cost functions and constraints. These designs generalize and extend those previously available, often achieving meaningful improvements. This approach can be used for a variety of other problems. Operating characteristics of the designs are also described.

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“…In the final section, we conclude with discussion of generalizations and observations concerning the results. While no work will be done here on cost model ii), note that it can be viewed as a staged allocation problem and hence can be optimized by the techniques developed in [9].…”

Section: Introductionmentioning

confidence: 99%

Response adaptive designs that incorporate switching costs and constraints

Hardwick

Stout

2007

Journal of Statistical Planning and Inference

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This paper examines the design and performance of sequential experiments where extensive switching is undesirable. Given an objective function to optimize by sampling between Bernoulli populations, two different models are considered. The constraint model restricts the maximum number of switches possible, while the cost model introduces a charge for each switch. Optimal allocation procedures and a new "hyperopic" procedure are discussed and their behavior examined. For the cost model, if one views the costs as control variables then the optimal allocation procedures yield the optimal tradeoff of expected switches vs. expected value of the objective function.Our approach is quite general, applying to any objective function, and gives users flexibility in incorporating practical considerations in the design of experiments. To illustrate the effects of the switching restrictions, they are applied to the problems of minimizing failures and of minimizing the Bayes risk in a nonlinear estimation problem. It is observed that when there are no restrictions the expected number of switches in the optimal allocation grows approximately as the square root of the sample size, for sample sizes up to a few hundred. It is also observed that one can dramatically reduce the number of switches without substantially affecting the expected value of the objective function. The adaptive hyperopic procedure is introduced and it is seen to perform nearly as well as the optimal procedure. Thus one need sacrifice only a small amount of statistical objective in order to achieve significant gains in practicality. We also examine scenarios in which switching is desirable, even beyond that which would occur in the optimal design, and show that similar computational approaches can be applied.

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Optimal few-stage designs

Cited by 32 publications

References 24 publications

Maximizing Quality of Information From Multiple Sensor Devices: The Exploration vs Exploitation Tradeoff

Maximizing Quality of Information From Multiple Sensor Devices: The Exploration vs Exploitation Tradeoff

Optimal screening designs with flexible cost and constraint structures

Response adaptive designs that incorporate switching costs and constraints

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