We present two data-driven methods to learn uncertainty sets in decision-making problems affected by uncertain data. In the first part of this talk, we introduce mean robust optimization (MRO), a general framework that uses machine learning clustering to bridge between robust and Wasserstein distributionally robust optimization. MRO builds uncertainty sets constructed based on clustered data rather than on observed data points directly, thereby significantly reducing problem size. We show finite-sample performance guarantees and explicitly control the potential pessimism introduced by any clustering procedure. We illustrate the benefits of our framework on several numerical examples, obtaining multiple orders of magnitude computational speedups with little-to-no effect on the solution quality. In the second part of the talk, we introduce a learning technique to automatically reshape and resize the uncertainty sets in robust optimization. This method relies on differentiating the solution of robust optimization problems with respect to the parameters defining the uncertainty sets. Our approach is very flexible, and it can learn a wide variety of uncertainty sets while preserving tractability. We implemented our work in LRO, a software package to naturally express decision-making problems affected by uncertain data and to automatically learn the corresponding robust optimization formulations. Numerical experiments in portfolio optimization, optimal control, and inventory management show that our method outperforms traditional approaches in robust optimization in terms of out of sample performance and constraint satisfaction guarantees.
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