Optimal Transport for Distributionally Robust Optimization and Applications in Machine Learning

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, optimal decisions of OT-based DRO problems can often be computed by solving tractable convex optimization problems. In this talk, we will show that OT-based DRO offers a principled approach to dealing with distribution shifts and heterogeneous data sources, and we will highlight new applications of OT-based DRO in responsible artificial intelligence. Finally, we will argue that, while OT is useful for DRO, ideas from DRO can also help us to solve challenging OT problems.