A General Wasserstein Framework for Data-driven Distributionally Robust Optimization: Tractability and Applications

Understand

Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors.

• An increasingly popular approach, known as Wasserstein distributionally robust optimization (DRO), achieves this by applying the Wasserstein metric to construct a ball centred at the empirical distribution and finding a solution that performs well against the most adversarial distribution from the ball.
• In this paper, we present a general framework for studying different choices of a Wasserstein metric and point out the limitation of the existing choices.
• In particular, while choosing a Wasserstein metric of a higher order is desirable from a data-driven perspective, given its less conservative nature, such a choice comes with a high price from a robustness perspective - it is no longer applicable to many heavy-tailed distributions of practical concern.