496 / 2024-04-25 16:07:58

On the Equivalence and Performance of DRO and RS Models in OM Applications

Distributionally robust optimization, robust satisficing, hyperparameter tuning, cross-validation

Distributionally robust optimization (DRO) has become ubiquitous to address uncertainties inherent in many operations management (OM) problems.

Recently, an alternative goal-driven framework, robust satisficing (RS), is proposed. Robust satisficing aims to attain a prescribed target, such as avoiding overshooting the cost budget as much as possible under uncertainty. The goal-driven modeling philosophy naturally fits many OM problems, yet there is a lack of direct comparisons between DRO and RS in OM applications. In this paper, we uncover connections between DRO and RS. Suppose both models are based on the Wasserstein metric and consider a risk-aware convex objective function affected by uncertain parameters. We demonstrate that they share the same solution family. We establish the correspondence between the radius parameter in DRO and the target parameter in RS such that the optimal solutions to the two models are the same.

Inspired by the globalized distributionally robust counterpart (GDRC), we extend the analysis to  GDRC and the globalized robust satisficing (GRS). We reveal that GDRC and GRS have the same solution families as DRO and RS, respectively. More importantly, we establish novel results on the equivalence of DRO, GDRC, RS, and GRS models under previously stated conditions. Although the equivalence result holds, the performance of the DRO and RS models can vary depending on how the model parameters are selected. The experiment results show that the use of cross-validation can reflect the actual model preference when data is sufficient.