Info-gap’s robustness model

According to info-gap decision theory, the robustness of decision x\in X is defined as follows:

\displaystyle \rho(x,\tilde{u}):= \max_{\rho\ge 0}\ \{\rho: r^{*}\le r(x,u),\forall u\in N(\rho,\tilde{u})\}

where

  • X = decision space.
  • u = parameter of interest whose true value is subject to severe uncertainty.
  • \tilde{u} = point estimate of the true value of u.
  • N(\rho,\tilde{u}) = neighborhood of size \rho around \tilde{u}.
  • r^{*} = critical performance level.
  • r(x,u) = performance level of decision x associated with the given value of u.

The greater the value of \rho(x,\tilde{u}), the more robust the decision.

This is illustrated by the following picture, where the neighborhoods are represented by the circles. Thus, the robustness of decision x is the radius of the largest circle centered at \tilde{u} such that the performance constraint r^{*}\le r(x,u) is satisfied for all value of u in the circle.

In short, info-gap’s robustness model is a re-invention of the radius of stability model (circa 1960).

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