Info-gap decision theory
Info-gap decision theory seeks to optimize robustness to failure under severe uncertainty,[1][2] in particular applying sensitivity analysis of the stability radius type[3] to perturbations in the value of a given estimate of the parameter of interest.
It has some connections with Wald's maximin model; some authors distinguish them, others consider them instances of the same principle.
It was developed by Yakov Ben-Haim,[4] and has found many applications and described as a theory for decision-making under "severe uncertainty".
It has been criticized as unsuited for this purpose, and alternatives proposed, including such classical approaches as robust optimization.
[citation needed] Another engineering application involves the design of a neural net for detecting faults in a mechanical system, based on real-time measurements.
They use info-gap robustness curves to select among management options for spruce-budworm populations in Eastern Canada.
Info-gap robustness and opportuneness analyses can assist in portfolio design, credit rationing, and other applications.
A more general criticism of decision making under uncertainty is the impact of outsized, unexpected events, ones that are not captured by the model.
Since stability radius models are designed for the analysis of small perturbations in a given nominal value of a parameter, Sniedovich[3] argues that info-gap's robustness model is unsuitable for the treatment of severe uncertainty characterized by a poor estimate and a vast uncertainty space.
Limitations on knowledge, understanding, and computational capability constrain the ability of decision makers to identify optimal choices.
Schwartz,[49] Conlisk [50] and others discuss extensive evidence for the phenomenon of bounded rationality among human decision makers, as well as for the advantages of satisficing when knowledge and understanding are deficient.
The info-gap robustness function provides a means of implementing a satisficing strategy under bounded rationality.
For instance, in discussing bounded rationality and satisficing in conservation and environmental management, Burgman notes that "Info-gap theory ... can function sensibly when there are 'severe' knowledge gaps."
The info-gap robustness and opportuneness functions provide "a formal framework to explore the kinds of speculations that occur intuitively when examining decision options."
[51] Burgman then proceeds to develop an info-gap robust-satisficing strategy for protecting the endangered orange-bellied parrot.
A number of authors have noted and discussed similarities and differences between info-gap robustness and minimax or worst-case methods [7][16][35][37] [53] .
[54] Sniedovich [47] has demonstrated formally that the info-gap robustness function can be represented as a maximin optimization, and is thus related to Wald's minimax theory.
This critical question clearly raises the issue of whether robustness (as defined by info-gap theory) is qualified to judge whether confidence is warranted,[5][55] [56] and how it compares to methods used to inform decisions under uncertainty using considerations not limited to the neighborhood of a bad initial guess.
These methods directly address decision under severe uncertainty, and have been used for this purpose for more than thirty years now.
In sharp contrast, robust optimization methods set out to incorporate in the analysis the entire region of uncertainty, or at least an adequate representation thereof.
Classical decision theory,[63][64] offers two approaches to decision-making under severe uncertainty, namely maximin and Laplaces' principle of insufficient reason (assume all outcomes equally likely); these may be considered alternative solutions to the problem info-gap addresses.
As attested by the rich literature on robust optimization, maximin provides a wide range of methods for decision making in the face of severe uncertainty.
As for Laplaces' principle of insufficient reason, in this context it is convenient to view it as an instance of Bayesian analysis.
The essence of the Bayesian analysis is applying probabilities for different possible realizations of the uncertain parameters.
In the case of Knightian (non-probabilistic) uncertainty, these probabilities represent the decision maker's "degree of belief" in a specific realization.
Nevertheless, methodologically speaking, this difficulty is not as problematic as basing the analysis of a problem subject to severe uncertainty on a single point estimate and its immediate neighborhood, as done by info-gap.
