# 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).