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A framework for optimization under limited information

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  • Tansu Alpcan

Abstract

In many real world problems, optimisation decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of data points. The scarcity of data may be due to high cost of observation or fast-changing nature of the underlying system. This paper presents a “black-box” optimisation framework that takes into account the information collection, estimation, and optimisation aspects in a holistic and structured manner. Explicitly quantifying the observations at each optimisation step using the entropy measure from information theory, the often nonconvex-objective function to be optimised is modelled and estimated by adopting a Bayesian approach and using Gaussian processes as a state-of-the-art regression method. The resulting iterative scheme allows the decision maker to address the problem by expressing preferences for each aspect quantitatively and concurrently. Copyright Springer Science+Business Media, LLC. 2013

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  • Tansu Alpcan, 2013. "A framework for optimization under limited information," Journal of Global Optimization, Springer, vol. 55(3), pages 681-706, March.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:3:p:681-706
    DOI: 10.1007/s10898-012-9942-z
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    References listed on IDEAS

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    1. D. Huang & T. Allen & W. Notz & N. Zeng, 2006. "Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models," Journal of Global Optimization, Springer, vol. 34(3), pages 441-466, March.
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    2. Michael Dreyfuss & Irit Nowik, 2020. "A puzzled driver is a better driver: enforcing speed limits using a randomization strategy," Journal of Global Optimization, Springer, vol. 76(3), pages 645-660, March.

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