Revealing Decision Conservativeness Through Inverse Distributionally Robust Optimization

TL;DR

This paper proposes Inverse Distributionally Robust Optimization (I-DRO) to infer decision-makers' conservativeness levels from their robust optimization decisions, providing a novel approach to understanding decision behavior under uncertainty.

Contribution

The paper introduces I-DRO as a new method to recover the conservativeness level in F-DRO using KKT conditions, with guarantees of solution uniqueness and applicability to power system scheduling.

Findings

I-DRO can accurately recover conservativeness levels in normal scenarios.

The method guarantees unique and optimal solutions under certain conditions.

Performance is validated on IEEE 5-bus and NYISO 11-zone systems.

Abstract

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.