On the Interplay of Optimal Transport and Distributionally Robust Optimization
Seminar in Insurance and Economics
SPEAKER: Daniel Kuhn (EPFL).
TITLE: On the Interplay of Optimal Transport and Distributionally Robust Optimization.
ABSTRACT: Optimal Transport (OT) seeks the most efficient way to morph one probability distribution into another one, and Distributionally Robust Optimization (DRO) studies worst-case risk minimization problems under distributional ambiguity. It is well known that OT gives rise to a rich class of data-driven DRO models, where the decision-maker plays a zero-sum game against nature who can adversely reshape the empirical distribution of the uncertain problem parameters within a prescribed transportation budget. Even though generic OT problems are computationally hard, the Nash strategies of the decision-maker and nature in OT-based DRO problems can often be computed efficiently. In this talk we will uncover deep connections between robustification and regularization, and we will disclose striking properties of nature’s Nash strategy, which implicitly constructs an adversarial training dataset. We will also show that OT-based DRO offers a principled approach to deal with distribution shifts and heterogeneous data sources, and we will highlight new applications of OT-based DRO in machine learning, statistics, risk management and control. Finally, we will argue that, while OT is useful for DRO, ideas from DRO can also help us to solve challenging OT problems.