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Reviews of publications on Info-Gap decision theory

Review # 9 (Posted: April 27, 2009; Last update: May 10, 2009)

Reference: Lior Davidovitch, Richard Stoklosa, Jonathan Majer, Alex Nietrzeba, Peter Whittle, Kerrie Mengersen, Yakov Ben-Haim.
Info-gap theory and robust design of surveillance for invasive species: The case study of Barrow Island
Journal of Environmental Management, Volume 90, Issue 8, Pages 2785-2793, 2009.
Abstract Surveillance for invasive non-indigenous species (NIS) is an integral part of a quarantine system. Estimating the efficiency of a surveillance strategy relies on many uncertain parameters estimated by experts, such as the efficiency of its components in face of the specific NIS, the ability of the NIS to inhabit different environments, and so on. Due to the importance of detecting an invasive NIS within a critical period of time, it is crucial that these uncertainties be accounted for in the design of the surveillance system. We formulate a detection model that takes into account, in addition to structured sampling for incursive NIS, incidental detection by untrained workers. We use info-gap theory for satisficing (not minimizing) the probability of detection, while at the same time maximizing the robustness to uncertainty. We demonstrate the trade-off between robustness to uncertainty, and an increase in the required probability of detection. An empirical example based on the detection of Pheidole megacephala on Barrow Island demonstrates the use of info-gap analysis to select a surveillance strategy.
Acknowledgement This work was initiated during the "Workshop on Surveillance and Uncertainty", in Hobart, Tasmania, which was sponsored by the Australian Centre for Excellence in Risk Analysis. Support from the CRC for National Plant Biosecurity is also acknowledged.
Scores TUIGF:100%
SNHNSNDN:100%
GIGO:120%


This is a typical Info-Gap article that repeats the standard errors, misconceptions and misleading information, associated with Info-Gap. It makes no reference whatsoever to the Maximin connection thus giving the reader the false impression that the model offered here is "different". It makes no reference whatsoever to the thriving literature on Robust Optimization thus depriving the reader of the knowledge about the wider context in which it belongs. But worse than all is the absence of any discussion on the localness of Info-Gap's robustness analysis. This gives the reader a thoroughly wrong idea of the results yielded by this analysis. I should therefore point out in this regard that it is this local treatment of severe uncertainty — especially "true" Knightian uncertainty — that makes Info-Gap decision theory a classic example of a voodoo decision theory.

These aspects of Info-Gap decision theory are discussed in detail in Faqs about Info-Gap decision theory. So here I shall comment only on three issues.

1. Satisficing vs Optimizing

This article continues to perpetuate the myth of the superiority of "satisficing" vs "optimizing" — by now a fixture in the Info-Gap literature — apparently aimed to justify Info-Gap's so called "robust satisficing" strategy. "Optimal decisions" — so the argument goes — are inferior to "satisficing decisions" because optimal decisions are not robust, namely they have zero robustness (page 4, emphasis is mine):

Another immediate result is that the robustness of the optimal result — the maximal reward under our best estimate û — is not robust. In fact, it has zero robustness, meaning that a slight deviation from our estimation û may prevent us from meeting the requirement rc. Note that the optimal result also has zero opportuneness, since it is achieved without deviating from the estimate.

To see how erroneous hence badly misleading this contention is, let us first get clear on what this thesis actually maintains. Consider then the following two optimization problems:

Problem A     Problem B
Optimal Reward ProblemRobust Satisficing Problem
  z*(û):= max   R(q,û)  
q∈Q
  α(rc,û):= max   max {α≥0: R(q,u) ≥ rc , ∀u∈U(α,û)}  
q∈Q

Let q' denote the optimal decision in the framework of Problem A and let q'' denote the optimal decision in the framework of Problem B.

Thus, according to Info-Gap decision theory, the robustness of these decisions is, by definition, as follows:

α(q',rc,û):= max {α ≥ 0: R(q',u) ≥ rc , ∀u∈U(α,û)}

α(q'',rc,û):= max {α ≥ 0: R(q'',u) ≥ rc , ∀u∈U(α,û)}

Clearly then, since q'' is optimal with respect to Problem B, its robustness cannot be smaller than the robustness of q', namely α(q'',rc,û) = α(rc,û) ≥ α(q',rc,û).

But this does not imply that the robustness of q' is zero. Indeed, the following example shows that the authors' claim that q' has zero robustness meaning that a slight deviation from our estimation û may prevent us from meeting the requirement rc is false.

Counter Example # 1

Consider the case where u is a scalar, û=0, Q={q',q''}, U(α,û)={u: |u-û| ≤ α, |u|≤4}, rc = 0.5 and R(q,u) is as follows:

So q' is optimal with respect to Problem A and q'' is optimal with respect to Problem B. The robustness of q' is equal to 3.5 and the robustness of q'' is equal to 3.8. In short, not only that the robustness of q' is not equal to zero, it is actually on a par with the robustness of q''.

But to bring out more forcefully how absurd the authors' claim is, consider the case where the optimal decision yielded by Problem A is also optimal for Problem B. In such cases not only is the robustness of q' not equal to zero, q' is in fact the most robust decision!!!!!!!!!!!!!

The following example illustrates this obvious point.

Counter Example # 2

Consider the case where u is a scalar, û=0, Q={q(1),q(2)}, U(α,û)={u: |u-û| ≤ α, |u|≤4}, rc = 1 and R(q,u) is as follows:

Clearly, q(1) dominates q(2) for all u in U=[-4,4], hence q(1) is optimal for both Problem A and Problem B. Therefore, we set q'=q''=q(1).

So not only is it the case that the robustness of q' is not zero, q' is the most robust decision!

The following example is designed to illustrate how confusion reigns, in this article, over the difference between what the authors call "optimal reward" and the violation of the performance requirement R(q,u) ≥ rc.

Counter Example # 3

Consider the case where u is a scalar, û=0, Q={q(1),q(2)}, U(α,û)={u: |u-û| ≤ α, |u|≤4}, rc = 0.5 and R(q,u) is as follows:

Note that in the region [û,4], a slight decrease in the value of u decreases slightly the value of the reward R(q',u). But this does not imply that a slight change in u in the neighborhood of the estimate û will violate the performance requirement R(q',u) ≥ rc=0.5.

Also note that q'' has the same feature: in the region [-4,û], a slight increase in the value of u decreases slightly the reward R(q'',u). But this does not imply that a slight change in u in the neighborhood of the estimate û will violate the performance requirement R(q'',u) ≥ rc=0.5.

Regarding robustness, q' is almost as robust as q'', noting that α(q',rc,û)=1 and α(q'',rc,û)=1.108.

Clearly, the authors' claim is false in this case.

I take this opportunity to illustrate the real consequences of Info-Gap's robustness analysis. As you will recall, one of Info-Gap's main failings is that its robustness definition, hence analysis, hence verdicts, are local. This failing renders it thoroughly unsuitable for the treatment of severe uncertainty. The following example illustrates this point.

Counter Example # 4

Consider the case where u is a scalar, û=0, Q={q',q''}, U(α,û)={u∈ℜ: |u-û| ≤ α}, rc = 3 and R(q,u) is defined as follows:
R(q',u) := 4.2 + 6u2 -6|u|

R(q'',u) := 3.4 - 4u2

The picture is this:

Clearly, the authors' claim is false here.

Moreover, Info-Gap's robustness model selects q'' as the optimal (most robust) decision and assesses it to be more robust than q' despite the fact that R(q',u) > R(q'',u) almost everywhere in the unbounded region of uncertainty U=ℜ, the exception being the tiny intervals [-0.4,-0.2] and [0.2,0.4].

In short, Info-Gap decision theory ranks decisions according to their robustness (in the neighborhood of the estimate û) where robustness is determined with respect to the performance requirement R(q,u) ≥ rc. Therefore, in comparing the robustness of decisions, the same value must be assigned to rc in the comparison. Otherwise the comparison is rendered meaningless.

The only conclusion that can be drawn from all this is that Problem A typically yields decisions that generate larger rewards in the immediate neighborhood of the estimate, whereas Problem B typically yields decisions that are more robust in the neighborhood of the estimate. But this in no way implies that q' is inferior to q''. All that is implied here is that q' is different from q''. The only way to decide between q' and q'' would be by conducting a Pareto trade-off between reward and robustness that are representative of the complete region of uncertainty.

So the bottom line is this: if the problem under consideration is such that the stated objective is to maximize robustness subject to a performance requirement, then clearly an optimal decision that is obtained for a different problem altogether — for instance the maximization of the performance function — should not be expected to be optimal with respect to the problem under consideration. This triviality does not demonstrate that satisficing is "better" than optimizing (see discussion on this triviality in FAQ # 68).

The following quote is very relevant here. It is taken from the last paragraph of Jan Odhnoff's (1965) paper (emphasis is mine):

It seems meaningless to draw more general conclusions from this study than those presented in section 2.2. Hence, that section maybe the conclusion of this paper. In my opinion there is room for both 'optimizing' and 'satisficing' models in business economics. Unfortunately, the difference between 'optimizing' and 'satisficing' is often referred to as a difference in the quality of a certain choice. It is a triviality that an optimal result in an optimization can be an unsatisfactory result in a satisficing model. The best things would therefore be to avoid a general use of these two words.
Jan Odhnoff
On the Techniques of Optimizing and Satisficing
The Swedish Journal of Economics
Vol. 67, No. 1 (Mar., 1965)
pp. 24-39

I fully sympathize with Odhnoff's frustration.

And to round out the discussion on the muddled arguments that are often advanced in the Info-gap literature regarding the distinct differences between Info-Gap's so-called "robust satisficing" strategy and some alleged "direct optimization strategy"; and the presumed great merits attributed to Info-Gap "robust satisficing" strategy, consider again the formulation of the two problems in question:

Problem A     Problem B
Optimization of reward Optimization of robustness
z*(û):= max   R(q,û)
q∈Q
  α(rc,û):= max   max {α≥0: R(q,u) ≥ rc , ∀u∈U(α,û)}  
q∈Q

For one thing, as brought out by this juxtaposition, the depiction of Info-Gap's robustness model as a "satisficing model" — as opposed to an "optimization model" — is grossly misleading.

Info-gap's robustness model is defintely an optimization model, one that seeks to maximize robustness. For another, the great fuss about Info-Gap's "satisficing robustness" is equally misleading. There is nothing unusual in constraints being incorporated in optimization models. In fact, this is common practice in optimization. So if robustness is a consideration, it would be duly incorporated in the formulation of the optimization problem considered, either as an objective to be maximized or as a constraint to be satisfied.

Indeed, the Pareto-tradeoff conducted by Info-Gap decision theory can be carried out in two different ways:

Observe that in both cases the problem is a (constrained) optimization problem and not merely a "satisficing" problem. In particular, the problem represented by Info-Gap's robustness model — namely Problem B — is a constrained maximization problem: it involves maximizing the deviation (α) from the estimate subject to a performance constraint.

The irony is that often it is actually easier to conduct the Pareto-tradeoff analysis by treating performance as an objective and robustness as a constraint!

Sadly, the triviality regarding "satisficing vs optimizing" discussed by Jan Odhnoff (1965) more than forty years ago continues to be propagated in the Info-Gap literature, including the article under review here. This contributes nothing to good environmental management.

It is regrettable that this muddle continues to be propagated in the Info-Gap literature.

Remark: Since any "satisficing problem" can easily be re-formulated as an equivalent "optimizing problem", the issue here is not whether it is better to optimize or satisfice. Rather, the issue is what should be optimized and what should be satisficed.

2. Incorporating "beliefs" in Info-Gap's uncertainty model

Info-Gap decision theory prides itself on being non-probabilistic and likelihood-free (see Review 6). So on what grounds do the authors claim that (page 4, emphasis is mine):

As the horizon of uncertainty α gets larger, the sets U(α,û) become more inclusive. The info-gap model expresses the decision maker's beliefs about uncertain variation of u around û.

As indicated in Review 6, Ben-Haim bans any imputation of "likelihood" to Info-Gap's uncertainty model. So, how does this statement sit with Ben-Haim's position on likelihood?

But more than this, any imputation of "belief" to Info-Gap's uncertainty model is in stark contradiction to Ben-Haim's own exhortations explicitly banning "belief" from the model. For example, in his book, Ben-Haim (2006, p. 22) notes the following (emphasis is mine):

Uncertainty is the potential for deviation of an actual realization from its normative form. Neither norm nor any specific potential realization is uncertain; it is the potential for deviation of one from the other which is info-gap uncertainty.

The spatial analogy for info-gap uncertainty demonstrates that we need no concept of chance, frequency of recurrence, likelihood, plausibility or belief in order to speak of uncertainty.

Ben Haim (2006, p. 22)

And how about this?

Since the horizon of uncertainty is unknown and unbounded, there is no worst case. Since no measure functions of probability (or plausibility, or belief, etc.) are specified by an info-gap model, the analyst cannot calculate statistical expectations and cannot probabilistically insure against the unknown contingencies identified in the info-gap model.
Ben-Haim Y. and Jeske, K. (2003, p. 12)
Bias in Financial Markets: Robust Satisficing with Info Gaps
FRB of Atlanta Working Paper No. 2003-35.
Available at SSRN: http://ssrn.com/abstract=487585

And this:

Info-gap models are axiomatically utterly different from both probability and fuzzy logic, since info-gap models focus on the set-structure of uncertainty rather than on measure-theoretical representations. Info-gap models are particularly suited to representing sparse information since they make no assertions about frequencies of, or beliefs about, rare events.
Ben-Haim Y (2002, November 5)
Quote from the abstract of a seminar at MIT
entitled: Info-Gap Decision Theory For Design And Planning Or: Why 'Good' Is Preferable To 'Best'

And this:

Info-gap models are axiomatically utterly different from both probability and fuzzy logic, since info-gap models focus on the set-structure of uncertainty rather than on measure-theoretical representations. Info-gap models are particularly suited to representing sparse information since they make no assertions about frequencies of, or beliefs about, rare events.
Ben-Haim Y (2003, June 5)
Quote from the abstract of a seminar at Los Alamos National Lab
entitled: Info-gap decision theory for design and planning

Suppose, however, that we ignore this blatant contradiction.

What should be made explicit in the Info-Gap literature is the following: what "beliefs" are expressed by Info-Gap's robustness model? For instance, what "beliefs" are represented by say

U(α,û)={u∈ℜ: |u - û| ≤ α} , α ≥ 0

and where exactly are "beliefs" of this type described in the two Info-Gap books, or elsewhere in the Info-Gap literature?

Suppose, for example, that in the context of this model û=0 so that

U(α,û)={u∈ℜ: |u| ≤ α} , α ≥ 0

and that this model is based on our initial "beliefs" regarding uncertain variation of u around û=0. How would we modify this model to account for the fact that our "beliefs" regarding uncertain variation of u around û=0 have changed?

More importantly, where do we find, in the Info-Gap literature, guidelines instructing how to incorporate "beliefs" in the construction of Info-Gap's model of uncertainty?

As for the problem under investigation in the article, what exactly are the "beliefs" that are expressed by the regions of uncertainty defined in the article by eq. (9)? Where are these "beliefs" described and quantified in the article?

Does this statement indicate that Info-Gap's uncertainty model expresses the "belief" that values of u near the estimate û are more likely or more "believable" than values of u that are further from û? If this is indeed so, then what is all this talk about severe uncertainty and on what grounds do the authors claim the following (page 4, emphasis is mine)?

Info-gap models are used to quantify non-probabilistic "true" (Knightian) uncertainty (Ben-Haim, 2006).

I urge the authors to examine Hall and Harvey's (2009) paper regarding this issue. The bottom line is this: Info-Gap's uncertainty model as such does not represent any "beliefs" whatsoever. Hence, any attribution of "belief" to the model must be carefully quantified and introduced formally as an additional assumption. For example, Hall and Harvey (2009) incorporate "likelihood" in Info-Gap's uncertainty model by explicitly adding the assumption (emphasis is mine):

An assumption remains that values of u become increasingly unlikely as they diverge from û.

Is this the kind of "beliefs" the authors have in mind? If so, they must state this in so many words.

Of course, as indicated in Review 6, the trouble with positing any such additional assumption is that it embroils the Info-Gap decision theory in yet greater difficulties. For, any assumption of this kind is utterly incompatible with the basic thesis that Info-Gap decision theory is designed specifically for the severest uncertainty imaginable, namely "true" Knightian uncertainty.

In summary.

The basic working assumption postulated by Info-Gap decision theory is that the estimate û is a wild guess, a poor indication of the true value of u, and is likely to be substantially wrong. This assumption is thoroughly correct, for it reflects the simple fact that Info-Gap decision theory is designed to manage severe uncertainty.

So whatever "belief" structure is imputed to Info-Gap's uncertainty model, the fact remains that the overwhelming "belief" is that the true value of u is "distant" from the estimate û. This is particularly the case — indeed, commonly the case — when the region of uncertainty, is unbounded. Indeed, if the "belief" is that the true value of u is in the neighborhood of the estimate, why should we care a straw about the region of uncertainty being unbounded?

In short, if the intention is indeed to modify Info-Gap's uncertainty model and let it express " ... the decision maker's "belief" about uncertain variation of u around û ..." then the authors must give an exact quantitative specification — as done for instance in Hall and Harvey (2009) — of this "belief" and then explain how this "belief" dwells under the same roof with the "true knightian" uncertainty that Info-Gap decision theory is supposed to deal with.

More importantly yet, perhaps, the authors would care to explain how such a quantification of "beliefs" is radically different (after normalization, if necessary) from say, the "beliefs" quantified by subjective probabilities, or the "beliefs" expressed by membership functions of fuzzy sets.

Be that as it may, the belief-based theory resulting from incorporating "beliefs" in Info-Gap's uncertainty model is clearly incongruous with Ben-Haim's Info-Gap theory.

3. How wrong can the estimate be?

On page 6 the authors state the following (emphasis is mine):

We will use info-gap analysis to estimate "how wrong can we be?", or how wrong can the estimates be, and still allow us to obtain an acceptable probability of detection.

As explained in FAQ # 28 and in Info-gap decision theory and the small applied world of environmental decision-making (Point 2), Info-Gap decision theory does not — much less can it — address such questions for the simple reason that the true value of u is unknown and is subject to severe uncertainty.

Rather, the question addressed by Info-Gap's robustness model is defined as follows:

How much can we deviate from the given estimate û so that the performance requirement is satisfied everywhere within the region of uncertainty stipulated by the deviation?

The following pictures illustrate the distinction between "being wrong" and "determining a safe deviation from the estimate".

Recall that Info-Gap's robustness model is defined as follows:

α(rc,û):= max   max {α≥0: R(q,u) ≥ rc , ∀u∈U(α,û)}
q∈Q

The picture is then as follow

No Man's LandûNo Man's Land
U(α(rc,û),û)
Safe

where the red area represents the "safe" region of uncertainty around the estimate and the "No Man's Land" is the region that is left unexplored by Info-Gap's robustness model.

The "size" of this safe area is α(rc,û) which means that the maximum safe deviation from the estimate is α(rc,û). In the picture this safe deviation is relatively small compared to the size of the complete region of uncertainty (shown in black).

That much is clear.

However, the whole point here is that the value of α(rc,û) gives us not the merest clue as to how "wrong" û is, and how wrong the points in the safe region are. The only way to establish how "wrong" these points are is to determine their "distance" from the true value of u. But this value is unknown and is subject to severe uncertainty.

For example, consider the case where the true value of u, denoted by u*, is at the far right hand-side of the region of uncertainty, as shown below:

No Man's LandûNo Man's Landu*
U(α(rc,û),û)
Safe  

Here the estimate is clearly "very wrong" as illustrated by its great distance from the true value of u.

The whole difficulty posed by severe uncertainty is that we have no inkling as to where u* is. This means that we have not the foggiest idea how wrong û is, and consequently how wrong can we be and still satisfy the performance requirement.

All we know is that the maximum "safe" deviation from the estimate is equal to α(rc,û).

In short: The authors confuse two completely different concepts:

It should be stressed that if the estimate û is poor, then the value of the largest safe deviation from the estimate is a poor indication of robustness against the uncertainty in the true value of u.

Remark: There are a number of distracting typos in the article. For instance, the term "minimizing" should be replaced by "maximizing" in the Abstract and Conclusions sections in relation to the probability of detection. Clearly, the objective is to maximize the probability of detection, not to minimize it.

Similarly, the term "decreases" should be replaced by "increases" at the end of Section 4 in the discussion on what constitutes a more demanding critical level of performance rc. That is, insofar as the performance constraint R(q,u) ≥ rc is concerned, a more demanding rc is a larger rc. Hence, rc is more demanding when it increases rather than when it decreases. Indeed, when rc is sufficiently small, the performance constraint is superfluous and can be ignored.

Other Reviews

  1. Ben-Haim (2001, 2006): Info-Gap Decision Theory: decisions under severe uncertainty.

  2. Regan et al (2005): Robust decision-making under severe uncertainty for conservation management.

  3. Moilanen et al (2006): Planning for robust reserve networks using uncertainty analysis.

  4. Burgman (2008): Shakespeare, Wald and decision making under severe uncertainty.

  5. Ben-Haim and Demertzis (2008): Confidence in monetary policy.

  6. Hall and Harvey (2009): Decision making under severe uncertainty for flood risk management: a case study of info-gap robustness analysis.

  7. Ben-Haim (2009): Info-gap forecasting and the advantage of sub-optimal models.

  8. Yokomizo et al (2009): Managing the impact of invasive species: the value of knowing the density-impact curve.

  9. Davidovitch et al (2009): Info-gap theory and robust design of surveillance for invasive species: The case study of Barrow Island.

  10. Ben-Haim et al (2009): Do we know how to set decision thresholds for diabetes?

  11. Beresford and Thompson (2009): An info-gap approach to managing portfolios of assets with uncertain returns

  12. Ben-Haim, Dacso, Carrasco, and Rajan (2009): Heterogeneous uncertainties in cholesterol management

  13. Rout, Thompson, and McCarthy (2009): Robust decisions for declaring eradication of invasive species

  14. Ben-Haim (2010): Info-Gap Economics: An Operational Introduction

  15. Hine and Hall (2010): Information gap analysis of flood model uncertainties and regional frequency analysis

  16. Ben-Haim (2010): Interpreting Null Results from Measurements with Uncertain Correlations: An Info-Gap Approach

  17. Wintle et al. (2010): Allocating monitoring effort in the face of unknown unknowns

  18. Moffitt et al. (2010): Securing the Border from Invasives: Robust Inspections under Severe Uncertainty

  19. Yemshanov et al. (2010): Robustness of Risk Maps and Survey Networks to Knowledge Gaps About a New Invasive Pest

  20. Davidovitch and Ben-Haim (2010): Robust satisficing voting: why are uncertain voters biased towards sincerity?

  21. Schwartz et al. (2010): What Makes a Good Decision? Robust Satisficing as a Normative Standard of Rational Decision Making

  22. Arkadeb Ghosal et al. (2010): Computing Robustness of FlexRay Schedules to Uncertainties in Design Parameters

  23. Hemez et al. (2002): Info-gap robustness for the correlation of tests and simulations of a non-linear transient

  24. Hemez et al. (2003): Applying information-gap reasoning to the predictive accuracy assessment of transient dynamics simulations

  25. Hemez, F.M. and Ben-Haim, Y. (2004): Info-gap robustness for the correlation of tests and simulations of a non-linear transient

  26. Ben-Haim, Y. (2007): Frequently asked questions about info-gap decision theory

  27. Sprenger, J. (2011): The Precautionary Approach and the Role of Scientists in Environmental Decision-Making

  28. Sprenger, J. (2011): Precaution with the Precautionary Principle: How does it help in making decisions

  29. Hall et al. (2011): Robust climate policies under uncertainty: A comparison of Info-­-Gap and RDM methods

  30. Ben-Haim and Cogan (2011) : Linear bounds on an uncertain non-linear oscillator: an info-gap approach

  31. Van der Burg and Tyre (2011) : Integrating info-gap decision theory with robust population management: a case study using the Mountain Plover

  32. Hildebrandt and Knoke (2011) : Investment decisions under uncertainty --- A methodological review on forest science studies.

  33. Wintle et al. (2011) : Ecological-economic optimization of biodiversity conservation under climate change.

  34. Ranger et al. (2011) : Adaptation in the UK: a decision-making process.


Recent Articles, Working Papers, Notes

Also, see my complete list of articles
    Moshe's new book!
  • Sniedovich, M. (2012) Fooled by local robustness, Risk Analysis, in press.

  • Sniedovich, M. (2012) Black swans, new Nostradamuses, voodoo decision theories and the science of decision-making in the face of severe uncertainty, International Transactions in Operational Research, in press.

  • Sniedovich, M. (2011) A classic decision theoretic perspective on worst-case analysis, Applications of Mathematics, 56(5), 499-509.

  • Sniedovich, M. (2011) Dynamic programming: introductory concepts, in Wiley Encyclopedia of Operations Research and Management Science (EORMS), Wiley.

  • Caserta, M., Voss, S., Sniedovich, M. (2011) Applying the corridor method to a blocks relocation problem, OR Spectrum, 33(4), 815-929, 2011.

  • Sniedovich, M. (2011) Dynamic Programming: Foundations and Principles, Second Edition, Taylor & Francis.

  • Sniedovich, M. (2010) A bird's view of Info-Gap decision theory, Journal of Risk Finance, 11(3), 268-283.

  • Sniedovich M. (2009) Modeling of robustness against severe uncertainty, pp. 33- 42, Proceedings of the 10th International Symposium on Operational Research, SOR'09, Nova Gorica, Slovenia, September 23-25, 2009.

  • Sniedovich M. (2009) A Critique of Info-Gap Robustness Model. In: Martorell et al. (eds), Safety, Reliability and Risk Analysis: Theory, Methods and Applications, pp. 2071-2079, Taylor and Francis Group, London.
  • .
  • Sniedovich M. (2009) A Classical Decision Theoretic Perspective on Worst-Case Analysis, Working Paper No. MS-03-09, Department of Mathematics and Statistics, The University of Melbourne.(PDF File)

  • Caserta, M., Voss, S., Sniedovich, M. (2008) The corridor method - A general solution concept with application to the blocks relocation problem. In: A. Bruzzone, F. Longo, Y. Merkuriev, G. Mirabelli and M.A. Piera (eds.), 11th International Workshop on Harbour, Maritime and Multimodal Logistics Modeling and Simulation, DIPTEM, Genova, 89-94.

  • Sniedovich, M. (2008) FAQS about Info-Gap Decision Theory, Working Paper No. MS-12-08, Department of Mathematics and Statistics, The University of Melbourne, (PDF File)

  • Sniedovich, M. (2008) A Call for the Reassessment of the Use and Promotion of Info-Gap Decision Theory in Australia (PDF File)

  • Sniedovich, M. (2008) Info-Gap decision theory and the small applied world of environmental decision-making, Working Paper No. MS-11-08
    This is a response to comments made by Mark Burgman on my criticism of Info-Gap (PDF file )

  • Sniedovich, M. (2008) A call for the reassessment of Info-Gap decision theory, Decision Point, 24, 10.

  • Sniedovich, M. (2008) From Shakespeare to Wald: modeling wors-case analysis in the face of severe uncertainty, Decision Point, 22, 8-9.

  • Sniedovich, M. (2008) Wald's Maximin model: a treasure in disguise!, Journal of Risk Finance, 9(3), 287-291.

  • Sniedovich, M. (2008) Anatomy of a Misguided Maximin formulation of Info-Gap's Robustness Model (PDF File)
    In this paper I explain, again, the misconceptions that Info-Gap proponents seem to have regarding the relationship between Info-Gap's robustness model and Wald's Maximin model.

  • Sniedovich. M. (2008) The Mighty Maximin! (PDF File)
    This paper is dedicated to the modeling aspects of Maximin and robust optimization.

  • Sniedovich, M. (2007) The art and science of modeling decision-making under severe uncertainty, Decision Making in Manufacturing and Services, 1-2, 111-136. (PDF File) .

  • Sniedovich, M. (2007) Crystal-Clear Answers to Two FAQs about Info-Gap (PDF File)
    In this paper I examine the two fundamental flaws in Info-Gap decision theory, and the flawed attempts to shrug off my criticism of Info-Gap decision theory.

  • My reply (PDF File) to Ben-Haim's response to one of my papers. (April 22, 2007)

    This is an exciting development!

    • Ben-Haim's response confirms my assessment of Info-Gap. It is clear that Info-Gap is fundamentally flawed and therefore unsuitable for decision-making under severe uncertainty.

    • Ben-Haim is not familiar with the fundamental concept point estimate. He does not realize that a function can be a point estimate of another function.

      So when you read my papers make sure that you do not misinterpret the notion point estimate. The phrase "A is a point estimate of B" simply means that A is an element of the same topological space that B belongs to. Thus, if B is say a probability density function and A is a point estimate of B, then A is a probability density function belonging to the same (assumed) set (family) of probability density functions.

      Ben-Haim mistakenly assumes that a point estimate is a point in a Euclidean space and therefore a point estimate cannot be say a function. This is incredible!


  • A formal proof that Info-Gap is Wald's Maximin Principle in disguise. (December 31, 2006)
    This is a very short article entitled Eureka! Info-Gap is Worst Case (maximin) in Disguise! (PDF File)
    It shows that Info-Gap is not a new theory but rather a simple instance of Wald's famous Maximin Principle dating back to 1945, which in turn goes back to von Neumann's work on Maximin problems in the context of Game Theory (1928).

  • A proof that Info-Gap's uncertainty model is fundamentally flawed. (December 31, 2006)
    This is a very short article entitled The Fundamental Flaw in Info-Gap's Uncertainty Model (PDF File) .
    It shows that because Info-Gap deploys a single point estimate under severe uncertainty, there is no reason to believe that the solutions it generates are likely to be robust.

  • A math-free explanation of the flaw in Info-Gap. ( December 31, 2006)
    This is a very short article entitled The GAP in Info-Gap (PDF File) .
    It is a math-free version of the paper above. Read it if you are allergic to math.

  • A long essay entitled What's Wrong with Info-Gap? An Operations Research Perspective (PDF File) (December 31, 2006).
    This is a paper that I presented at the ASOR Recent Advances in Operations Research (PDF File) mini-conference (December 1, 2006, Melbourne, Australia).

Recent Lectures, Seminars, Presentations

If your organization is promoting Info-Gap, I suggest that you invite me for a seminar at your place. I promise to deliver a lively, informative, entertaining and convincing presentation explaining why it is not a good idea to use — let alone promote — Info-Gap as a decision-making tool.

Here is a list of relevant lectures/seminars on this topic that I gave in the last two years.


Disclaimer: This page, its contents and style, are the responsibility of the author (Moshe Sniedovich) and do not represent the views, policies or opinions of the organizations he is associated/affiliated with.


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