  Data-driven decision-making is performed by solving a parameterized
optimization problem, and the optimal decision is given by an optimal solution
for unknown true parameters. We often need a solution that satisfies true
constraints even though these are unknown. Robust optimization is employed to
obtain such a solution, where the uncertainty of the parameter is represented
by an ellipsoid, and the scale of robustness is controlled by a coefficient. In
this study, we propose an algorithm to determine the scale such that the
solution has a good objective value and satisfies the true constraints with a
given confidence probability. Under some regularity conditions, the scale
obtained by our algorithm is asymptotically $O(1/\sqrt{n})$, whereas the scale
obtained by a standard approach is $O(\sqrt{d/n})$. This means that our
algorithm is less affected by the dimensionality of the parameters.
