Revealing Decision Conservativeness Through Inverse Distributionally Robust Optimization

Qi Li, Zhirui Liang, Andrey Bernstein, Yury Dvorkin

Research output: Contribution to journalArticlepeer-review


This paper introduces Inverse Distributionally Robust Optimization (I-DRO) as a method to infer the conservativeness level of a decision-maker, represented by the size of a Wasserstein metric-based ambiguity set, from the optimal decisions made using Forward Distributionally Robust Optimization (F-DRO). By leveraging the Karush-Kuhn-Tucker (KKT) conditions of the convex F-DRO model, we formulate I-DRO as a bi-linear program, which can be solved using off-the-shelf optimization solvers. Additionally, this formulation exhibits several advantageous properties. We demonstrate that I-DRO not only guarantees the existence and uniqueness of an optimal solution but also establishes the necessary and sufficient conditions for this optimal solution to accurately match the actual conservativeness level in F-DRO. Furthermore, we identify three extreme scenarios that may impact I-DRO effectiveness. Our case study applies F-DRO for power system scheduling under uncertainty and employs I-DRO to recover the conservativeness level of system operators. Numerical experiments based on an IEEE 5-bus system and a realistic NYISO 11-zone system demonstrate I-DRO performance in both normal and extreme scenarios. An extended version of this paper with additional analyses is available at li2024revealing.
Original languageAmerican English
Pages (from-to)1018-1023
Number of pages6
JournalIEEE Control Systems Letters
StatePublished - 2024

NREL Publication Number

  • NREL/JA-5D00-90211


  • distributionally robust optimization
  • inverse optimization
  • optimal power flow
  • Wasserstein metric


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