Wasserstein Distributionally Robust Optimization - Theory and Applications in Machine Learning

Explore the theory and applications of Wasserstein Distributionally Robust Optimization in machine learning through this comprehensive lecture. Delve into data-driven decision-making challenges, learn about the Wasserstein distance approach, and discover its benefits in solving complex problems. Examine the connections between statistical learning and Wasserstein DRO, and understand its applications in classification, regression, maximum likelihood estimation, and minimum mean square error estimation. Gain insights into tractable convex optimization problems, out-of-sample guarantees, and asymptotic consistency in decision-making under uncertainty.

Intro
Decision-Making under Uncertainty
Data-Driven Decision-Making
Nominal Distribution
Estimation Errors
Wasserstein Distance
Stability Theory
Distributionally Robust Optimization (DRO)
Wasserstein DRO
Gelbrich Bound (p = 2)
Strong Duality
Piecewise Concave Loss
Main Takeaways
Warst-Case Risk for p = 1
Computing the Gelbrich Bound
Piecewise Quadratic Lass
Classification
Regression
Maximum Likelihood Estimation
Minimum Mean Square Error Estimation