# regret criterion

## regret criterion

[ri′gret krī‚tir·ē·ən]
(mathematics)
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The Minimax Regret Criterion. "Regret" is synonymous with the opportunity cost of not having made the best decision for a given outcome.
The minimax regret criterion was first described by Savage (1951) in the context of uncertainty over world states, and has been advocated more recently for robust decision making with incompletely specified utility functions (Boutilier, Bacchus, and Brafman 2001; Salo and Hamalainen 2001; Boutilier et al.
The minimax regret criterion can be used both for making robust decisions under strict uncertainty and for guiding the elicitation process itself.
Another rival decision theory is the minimax regret criterion. It focuses on the biggest disparity between parallel outcomes.(128) Worst-case outcomes are parallel to one another, as are best-case outcomes, and so on.
I will not venture to say here whether the maximin rule, the principle of insufficient reason, or the minimax regret criterion is universally the "most rational" under conditions of uncertainty.(129) Given the particular circumstances of the choice between a system with a guaranteed national forum and a system with no guaranteed national forum, I believe all three modes of decisionmaking point to the same result.
The same reasoning applies to the minimax regret criterion. The only scenario in which any regret would be suffered is the worst-case scenario, and the regret would be suffered by those choosing the system with no guaranteed national forum.
Assuming arguendo that this scenario were to develop, at most it would make the principle of insufficient reason and the minimax regret criterion indeterminate.
If the best-case scenario under the dual system was just slightly better, or if the best-case scenario under the unitary system was just slightly worse, the minimax regret criterion would be decisively in favor of the nonguaranteed national forum system.
The principles of insufficient reason and minimax regret criterion would then both be indecisive.
We have studied availabilities of Laplace criterion, Hurwicz criterion, min-max cost and min-max regret criterion [7-9].
We will name the min-max regret criterion the criterion of min-max risk or losses caused by uncertainty of information, because this criterion guarantees that maximum of losses from the uncertainty of information is as small as possible.
There are several possibilities to optimize loads of units under uncertainty (Laplace, Hurwicz, min-max cost, min-max regret criterions and others [12, 13].

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