A classical decision theoretic perspective on worst-case analysis. (English) Zbl 1249.91023

This refreshing article partly deviates from the majority of papers one can find in mathematical journals. Indeed, it is not common to quote a play by William Shakespeare in mathematics-oriented papers. The author clearly wishes to flavor his work by a pinch of philosophy.
The goal of the paper is to demonstrate that various seemingly different approaches to handling uncertain data, such as worst-case analysis, information-gap modeling, robust optimization or decision-making under uncertainty, can be formulated in a unified way as a maximin problem: Find \(z\in \mathbb{R}\) such that \[ z=\max _{d\in D} \min _{s\in S(d)} f(d,s), \] where \(D\) represents a decision space, \(S(d)\) denotes the set of states associated with the decisions \(d\in D\), and \(f\) stands for an objective function.


91B06 Decision theory
91A05 2-person games
90C47 Minimax problems in mathematical programming
68T37 Reasoning under uncertainty in the context of artificial intelligence
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