Explore cutting-edge data-driven methods for learning uncertainty sets in decision-making problems affected by uncertain data in this 49-minute lecture presented by Bartolomeo Stellato from Princeton University's Operations Research and Financial Engineering department. Dive into the mean robust optimization (MRO) framework, which bridges robust and Wasserstein distributionally robust optimization using machine learning clustering. Discover how MRO constructs uncertainty sets based on clustered data, significantly reducing problem size while maintaining solution quality. Learn about finite-sample performance guarantees and how to control potential pessimism introduced by clustering procedures. Examine a novel learning technique for automatically reshaping and resizing uncertainty sets in robust optimization, utilizing differentiation of robust optimization problem solutions. Gain insights into the LRO software package, designed to express decision-making problems with uncertain data and learn corresponding robust optimization formulations. Analyze numerical experiments in portfolio optimization, optimal control, and inventory management to understand how these methods outperform traditional robust optimization approaches in out-of-sample performance and constraint satisfaction guarantees. Read more