Resolve the comparison of DRO and RS in well-specified and over-specified shifts

Determine whether Distributionally Robust Optimization or Robust Satisficing yields the tighter aggregate trade-off term when the known-direction shift calibration is well-specified or over-specified, accounting for DRO’s vanishing sensitivity term and potentially larger regularization penalty relative to RS.

Background

In the known-direction setting, the paper calibrates the DRO radius and RS threshold using a nominal shift magnitude that may be smaller than, equal to, or larger than the true shift magnitude. When the nominal magnitude is at least the true magnitude, the DRO ambiguity set covers the target distribution, so the sensitivity component of the DRO bound vanishes.

However, the paper proves that the regularization penalty can favor RS because DRO hedges against every distribution in its ambiguity set, whereas RS is calibrated to a nominal target. The authors therefore state that the overall comparison is undecided in the well-specified and over-specified regimes; numerical results suggest that increasing over-specification may worsen DRO’s regularization cost, but no general ordering is established.