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From Statistical Decision Theory to Robust Optimization: A Maximin Perspective on Robust Decision-Making

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Robustness Analysis in Decision Aiding, Optimization, and Analytics

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 241))

Abstract

As attested by the prevalence of worst-case-based robustness analysis in many fields, Wald’s maximin paradigm (circa 1940) plays a central role in the broad area of decision-making under uncertainty. The objective of this chapter is therefore twofold. First, to examine the basic conceptual and modeling aspects of this ostensibly intuitive, yet controversial paradigm, so as to clarify some of the issues involved in its deployment in decision-making in the face of a non-probabilistic uncertainty. Second, to elucidate the differences between this paradigm and other maximin paradigms, such as those used in error analysis and game theory. We thereby chart the journey of this paradigm from the field of statistical decision theory to that of modern robust optimization, highlighting its use in the latter, as a tool for dealing with both local and global robustness. We also look briefly at the relationship between probabilistic and worst-case-based robustness analysis.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Melbourne, Melbourne, VIC, 3010, Australia

    Moshe Sniedovich

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  1. Moshe Sniedovich
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Correspondence to Moshe Sniedovich .

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Editors and Affiliations

  1. School of Production Engineering & Mgmt, Technical University of Crete, Chania, Greece

    Michael Doumpos

  2. School of Production Engineering & Mgmt, Technical University of Crete, Chania, Greece

    Constantin Zopounidis

  3. School of Production Engineering & Mgmt, Technical University of Crete, Chania, Greece

    Evangelos Grigoroudis

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Sniedovich, M. (2016). From Statistical Decision Theory to Robust Optimization: A Maximin Perspective on Robust Decision-Making. In: Doumpos, M., Zopounidis, C., Grigoroudis, E. (eds) Robustness Analysis in Decision Aiding, Optimization, and Analytics. International Series in Operations Research & Management Science, vol 241. Springer, Cham. https://doi.org/10.1007/978-3-319-33121-8_4

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