The knowledge-gradient stopping rule for ranking and selection

Frazier, Peter I.; Powell,

doi:10.1109/wsc.2008.4736082

Cited by 19 publications

(5 citation statements)

References 16 publications

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“…Usually there is a limited budget for evaluating the alternatives and when the budget is exhausted, the agent has to choose the alternative that appears to be the best, according to the obtained knowledge (Swisher, Jacobson, & Yücesan, 2003). Frazier and Powell (2008) present a version of this problem where the prior information units and the new obtained information units about each alternative are sampled from a specific distribution with unknown mean and variance. The model provides a new heuristic sampling and stopping rule that relies on the distribution of the samples.…”

Section: Exploration-exploitation Problemsmentioning

confidence: 99%

Decision Making with Dynamic Uncertain Events

Kalech

Reches

2015

jair

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When to make a decision is a key question in decision making problems characterized by uncertainty. In this paper we deal with decision making in environments where information arrives dynamically. We address the tradeoff between waiting and stopping strategies. On the one hand, waiting to obtain more information reduces uncertainty, but it comes with a cost. Stopping and making a decision based on an expected utility reduces the cost of waiting, but the decision is based on uncertain information. We propose an optimal algorithm and two approximation algorithms. We prove that one approximation is optimistic -waits at least as long as the optimal algorithm, while the other is pessimistic -stops not later than the optimal algorithm. We evaluate our algorithms theoretically and empirically and show that the quality of the decision in both approximations is near-optimal and much faster than the optimal algorithm. Also, we can conclude from the experiments that the cost function is a key factor to chose the most effective algorithm.

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Section: Exploration-exploitation Problemsmentioning

confidence: 99%

Decision Making with Dynamic Uncertain Events

Kalech

Reches

2015

jair

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“…Project members Warren Powell and Ilya Rhyzov have explored this problem of information collection on a graph and have found that they can adapt an existing knowledge gradient method [FrPo08] to this new problem. In computational testing they have found that for networks where the paths are not too short, the knowledge gradient works consistently quite well relative to competing techniques [RP09].…”

Section: Data Sampling Strategies For Sensor Datamentioning

confidence: 99%

Sensor Management Problems of Nuclear Detection

Carpenter

Cheng

Roberts

et al. 2011

Springer Series in Reliability Engineering

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Terrorist nuclear attack is a potentially devastating threat to homeland security. It is increasingly important to have the capability to intercept illicit nuclear materials entering the country and to monitor for nuclear threats emerging from within. This article describes a variety of approaches to sensor management in a multi-institution project on nuclear detection, which is based at Rutgers University and supported by the US Department of Homeland Security Domestic Nuclear Detection Office in collaboration with the US National Science Foundation. These approaches revolve around formulating the related problems using precise mathematical language and then developing tools of the mathematical sciences to solve them. The article provides an overview and summary of the project. In so doing, it touches on four themes that have emerged as the areas of greatest emphasis in the project: 1) methods to exploit data from radiation sensors and shipping manifests for classification and decision making; 2) ways to optimize sequential decisions in layered inspection processes; 3) detection using a fleet of mobile radiation sensors; and 4) data sampling strategies for nuclear detection.

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“…The work [4] provides an empirical study of several stopping rules. The work [19] combines the search for the next design point, at which the high-fidelity model is evaluated, with the number of iterations to perform, and solves the corresponding problem heuristically. The authors of [19] show that their stopping rule can stop too soon but that the incurred loss of stopping too soon is low.…”

mentioning

confidence: 99%

“…The work [19] combines the search for the next design point, at which the high-fidelity model is evaluated, with the number of iterations to perform, and solves the corresponding problem heuristically. The authors of [19] show that their stopping rule can stop too soon but that the incurred loss of stopping too soon is low. While a major challenge in stopping rules for Bayesian optimization is to forecast how much is gained by another adaptation, we will rely on rates that describe the error and costs behavior of our low-fidelity models to trade off costs and benefit.…”

mentioning

confidence: 99%

Multifidelity Monte Carlo Estimation with Adaptive Low-Fidelity Models

Peherstorfer¹

2019

SIAM/ASA J. Uncertainty Quantification

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Multifidelity Monte Carlo (MFMC) estimation combines low-and high-fidelity models to speedup the estimation of statistics of the high-fidelity model outputs. MFMC optimally samples the lowand high-fidelity models such that the MFMC estimator has minimal mean-squared error for a given computational budget. In the setup of MFMC, the low-fidelity models are static, i.e., they are given and fixed and cannot be changed and adapted. We introduce the adaptive MFMC (AMFMC) method that splits the computational budget between adapting the low-fidelity models to improve their approximation quality and sampling the low-and high-fidelity models to reduce the mean-squared error of the estimator. Our AMFMC approach derives the quasi-optimal balance between adaptation and sampling in the sense that our approach minimizes an upper bound of the mean-squared error, instead of the error directly. We show that the quasi-optimal number of adaptations of the lowfidelity models is bounded even in the limit case that an infinite budget is available. This shows that adapting low-fidelity models in MFMC beyond a certain approximation accuracy is unnecessary and can even be wasteful. Our AMFMC approach trades-off adaptation and sampling and so avoids over-adaptation of the low-fidelity models. Besides the costs of adapting low-fidelity models, our AMFMC approach can also take into account the costs of the initial construction of the low-fidelity models ("offline costs"), which is critical if low-fidelity models are computationally expensive to build such as reduced models and data-fit surrogate models. Numerical results demonstrate that our adaptive approach can achieve orders of magnitude speedups compared to MFMC estimators with static low-fidelity models and compared to Monte Carlo estimators that use the high-fidelity model alone.

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The knowledge-gradient stopping rule for ranking and selection

Cited by 19 publications

References 16 publications

Decision Making with Dynamic Uncertain Events

Decision Making with Dynamic Uncertain Events

Sensor Management Problems of Nuclear Detection

Multifidelity Monte Carlo Estimation with Adaptive Low-Fidelity Models

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