Info-gap decision theory seeks to optimize robustness to failure under severe uncertainty,Yakov Ben-Haim, Information-Gap Theory: Decisions Under Severe Uncertainty, Academic Press, London, 2001.Yakov Ben-Haim, Info-Gap Theory: Decisions Under Severe Uncertainty, 2nd edition, Academic Press, London, 2006. in particular applying sensitivity analysis of the stability radius type 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, 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.
Applications Info-gap theory has generated a lot of literature. Info-gap theory has been studied or applied in a range of applications including engineering,
Yakov Ben-Haim, 2005, Info-gap Decision Theory For Engineering Design. Or: Why `Good' is Preferable to `Best', appearing as chapter 11 in Engineering Design Reliability Handbook, Edited by Efstratios Nikolaidis, Dan M.Ghiocel and Surendra Singhal, CRC Press, Boca Raton.
Kaihong Wang, 2005, Vibration Analysis of Cracked Composite Bending-torsion Beams for Damage Diagnosis, PhD thesis, Virginia Politechnic Institute, Blacksburg, Virginia.
Izuru Takewaki and Yakov Ben-Haim, 2007, Info-gap robust design of passively controlled structures with load and model uncertainties, Structural Design Optimization Considering Uncertainties, Yiannis Tsompanakis, Nikkos D. Lagaros and Manolis Papadrakakis, editors, Taylor and Francis Publishers. biological conservation,
L. Joe Moffitt, John K. Stranlund and Craig D. Osteen, 2007, Robust detection protocols for uncertain introductions of invasive species, Journal of Environmental Management, In Press, Corrected Proof, Available online 27 August 2007.
Burgman, Mark, 2005, Risks and Decisions for Conservation and Environmental Management, Cambridge University Press, Cambridge. theoretical biology, homeland security, economics,John K. Stranlund and Yakov Ben-Haim, (2007), Price-based vs. quantity-based environmental regulation under Knightian uncertainty: An info-gap robust satisficing perspective, Journal of Environmental Management, In Press, Corrected Proof, Available online 28 March 2007. project management
and statistics. Foundational issues related to info-gap theory have also been studied.
George J. Klir, 2006, Uncertainty and Information: Foundations of Generalized Information Theory, Wiley Publishers. Yakov Ben-Haim, 2007, Peirce, Haack and Info-gaps, in Susan Haack, A Lady of Distinctions: The Philosopher Responds to Her Critics, edited by Cornelis de Waal, Prometheus Books.
Engineering A typical engineering application is the vibration analysis of a cracked beam, where the location, size, shape and orientation of the crack is unknown and greatly influence the vibration dynamics. Very little is usually known about these spatial and geometrical uncertainties. The info-gap analysis allows one to model these uncertainties, and to determine the degree of robustness - to these uncertainties - of properties such as vibration amplitude, natural frequencies, and natural modes of vibration. Another example is the structural design of a building subject to uncertain loads such as from wind or earthquakes. The response of the structure depends strongly on the spatial and temporal distribution of the loads. However, storms and earthquakes are highly idiosyncratic events, and the interaction between the event and the structure involves very site-specific mechanical properties which are rarely known. The info-gap analysis enables the design of the structure to enhance structural immunity against uncertain deviations from design-base or estimated worst-case loads. Another engineering application involves the design of a neural net for detecting faults in a mechanical system, based on real-time measurements. A major difficulty is that faults are highly idiosyncratic, so that training data for the neural net will tend to differ substantially from data obtained from real-time faults after the net has been trained. The info-gap robustness strategy enables one to design the neural net to be robust to the disparity between training data and future real events.
Biology The conservation biologist faces info-gaps in using biological models. They use info-gap robustness curves to select among management options for spruce-budworm populations in Eastern Canada. Burgman Burgman, Mark, 2005, Risks and Decisions for Conservation and Environmental Management, Cambridge University Press, Cambridge, pp.399. uses the fact that the robustness curves of different alternatives can intersect.
Project management Project management is another area where info-gap uncertainty is common. The project manager often has very limited information about the duration and cost of some of the tasks in the project, and info-gap robustness can assist in project planning and integration. Financial economics is another area where the future is unpredictable, which may be either pernicious or propitious. Info-gap robustness and opportuneness analyses can assist in portfolio design, credit rationing, and other applications.
Criticism A general criticism of non-probabilistic decision rules, discussed in detail at decision theory: alternatives to probability theory, is that optimal decision rules (formally, admissible decision rules) can always be derived by probabilistic methods, with a suitable utility function and prior distribution (this is the statement of the complete class theorems), and thus that non-probabilistic methods such as info-gap are unnecessary and do not yield new or better decision rules.
A more general criticism of decision making under uncertainty is the impact of outsized, unexpected events, ones that are not captured by the model. This is discussed particularly in black swan theory, and info-gap, used in isolation, is vulnerable to this, as are a fortiori all decision theories that use a fixed universe of possibilities, notably probabilistic ones.
Sniedovich raises two points to info-gap decision theory, one substantive, one scholarly: 1. the info-gap uncertainty model is flawed and oversold One should consider the range of possibilities, not its subsets. Sniedovich argues that info-gap decision theory is therefore a "voodoo decision theory." 2. info-gap is maximin Ben-Haim states (Ben-Haim 1999, pp. 271–2) that "robust reliability is emphatically not a [min-max] worst-case analysis". Note that Ben-Haim compares info-gap to minimax, while Sniedovich considers it a case of maximin.
Sniedovich has challenged the validity of info-gap theory for making decisions under severe uncertainty. Sniedovich notes that the info-gap robustness function is "local" to the region around , where is likely to be substantially in error.
Maximin Symbolically, max assuming min (worst-case) outcome, or maximin.
In other words, while it is not a maximin analysis of outcome over the universe of uncertainty, it is a maximin analysis over a properly construed decision space.
Ben-Haim argues that info-gap's robustness model is not min-max/maximin analysis because it is not worst-case analysis of outcomes; it is a satisficing model, not an optimization model – a (straightforward) maximin analysis would consider worst-case outcomes over the entire space which, since uncertainty is often potentially unbounded, would yield an unbounded bad worst case.
Stability radius
Sniedovich has shown that info-gap's robustness model is a simple stability radius model, namely a local stability model of the generic form
where denotes a ball of radius centered at and denotes the set of values of that satisfy pre-determined stability conditions.
In other words, info-gap's robustness model is a stability radius model characterized by a stability requirement of the form . Since stability radius models are designed for the analysis of small perturbations in a given nominal value of a parameter, Sniedovich 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.
Discussion
Satisficing and bounded rationality It is correct that the info-gap robustness function is local, and has restricted quantitative value in some cases. However, a major purpose of decision analysis is to provide focus for subjective judgments. That is, regardless of the formal analysis, a framework for discussion is provided. Without entering into any particular framework, or characteristics of frameworks in general, discussion follows about proposals for such frameworks.
Simon introduced the idea of bounded rationality. Limitations on knowledge, understanding, and computational capability constrain the ability of decision makers to identify optimal choices. Simon advocated satisficing rather than optimizing: seeking adequate (rather than optimal) outcomes given available resources. Schwartz,Schwartz, Barry, 2004, Paradox of Choice: Why More Is Less, Harper Perennial. Conlisk
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." Burgman, Mark, 2005, Risks and Decisions for Conservation and Environmental Management, Cambridge University Press, Cambridge, pp.391, 394. Burgman then proceeds to develop an info-gap robust-satisficing strategy for protecting the endangered orange-bellied parrot. Similarly, Vinot, Cogan and Cipolla discuss engineering design and note that "the downside of a model-based analysis lies in the knowledge that the model behavior is only an approximation to the real system behavior. Hence the question of the honest designer: how sensitive is my measure of design success to uncertainties in my system representation? ... It is evident that if model-based analysis is to be used with any level of confidence then ... [one must] attempt to satisfy an acceptable sub-optimal level of performance while remaining maximally robust to the system uncertainties." They proceed to develop an info-gap robust-satisficing design procedure for an aerospace application.
Alternatives Of course, decision in the face of uncertainty is nothing new, and attempts to deal with it have a long history. A number of authors have noted and discussed similarities and differences between info-gap robustness and minimax or worst-case methods
Z. Ben-Haim and Y. C. Eldar, Maximum set estimators with bounded estimation error, IEEE Trans. Signal Process., vol. 53, no. 8, August 2005, pp. 3172-3182. .Babuška, I., F. Nobile and R. Tempone, 2005, Worst case scenario analysis for elliptic problems with uncertainty, Numerische Mathematik (in English) vol.101 pp.185–219. Sniedovich