Calibration of Distributionally Robust Empirical Optimization Models

Abstract

<jats:p> In “Calibration of Robust Empirical Optimization Models,” Gotoh, Kim, and Lim study the statistical properties of ɸ-divergence distributionally robust optimization with concave rewards. They show that worst-case sensitivity of the expected reward to deviations from the nominal is equal to the in-sample variance and that significant out-of-sample variance (sensitivity) reduction is possible with little impact on the mean if the robustness parameter is properly chosen. The authors also explain theoretically why the out-of-sample expected reward of robust solutions can sometimes “beat” that of sample average optimization, a phenomenon that has been observed empirically, and that the difference is typically small. This paper highlights that robust solutions are not “too conservative” if both mean and variance (sensitivity) are considered when selecting the size of the uncertainty set (e.g., via the bootstrap). </jats:p>