Autonomy Talks - Bartolomeo Stellato: Learning for Decision-Making under Uncertainty

Autonomy Talks - 16/04/24

Speaker: Prof. Bartolomeo Stellato, Princeton University

Title: Learning for Decision-Making under Uncertainty

Abstract: We present two machine learning methods to learn uncertainty sets in decision-making problems affected by uncertain data. In the first part, we introduce mean robust optimization (MRO), a framework that constructs data-driven uncertainty sets based on clustered data rather than on observed data points directly. By varying the number of clusters, MRO balances computational complexity and conservatism, and effectively bridges robust and Wasserstein distributionally robust optimization. In the second part, we present LRO, a method to automatically learn the shape and size of the uncertainty sets in robust optimization. LRO optimizes the performance across a family of parametric problems, while guaranteeing a target probability of constraint satisfaction. It relies on a stochastic augmented Lagrangian method that differentiates the solutions of robust optimization problems with respect to the parameters of the uncertainty set. Our approach is very flexible, and it can learn a wide variety of uncertainty sets commonly used in practice. We illustrate the benefits of our two machine learning methods on several numerical examples, obtaining significant reductions in computational complexity and conservatism, while preserving out-of-sample constraint satisfaction guarantees.